Saudi Arabia, Egypt, United Arab Emirates and Bahrain cut relations with Qatar in a coordinated move. Yemen, Libya's eastern-based government and the Maldives joined in later.
Qatar denounced the move as based on lies about it supporting militants. It has often been accused of being a funding source for Islamists, as has Saudi Arabia.
Arab League Secretary-General Ahmed Aboul Gheit expressed regret that relations between Qatar and major regional powers had got to the point of suspending diplomatic relations.
Iran, long at odds with Saudi Arabia and a behind-the-scenes target of the move, blamed Trump's visit last month to Riyadh.
"What is happening is the preliminary result of the sword dance," Hamid Aboutalebi, deputy chief of staff of Iran's President Hassan Rouhani, tweeted in reference to Trump's joining in a traditional dance with the Saudi king at the meeting.
The diplomatic broadside threatens the international prestige of Qatar, home to a large US military base and set to host the 2022 World Cup.
The hawkish tone Trump brought in his visit to over 50 Muslim leaders in Saudi Arabia regarding Iran and on terrorism is seen as having laid the groundwork for the diplomatic crisis. It was unclear how it would affect the military base.
"You have a shift in the balance of power in the Gulf now because of the new presidency: Trump is strongly opposed to political Islam and Iran," said Jean-Marc Rickli, head of global risk and resilience at the Geneva Centre for Security Policy.
"He is totally aligned with Abu Dhabi and Riyadh, who also want no compromise with either Iran or the political Islam promoted by the Muslim Brotherhood."
Qatar has for years presented itself as a mediator and power broker for the region's many disputes, but Egypt and the Gulf Arab states resent Qatar's support for Islamists, especially the Muslim Brotherhood, which they see as a political foe.
Closing all transport ties with Qatar, the three Gulf states gave Qatari visitors and residents two weeks to leave.
In the harshest measures, Saudi Arabia and Bahrain's civil aviation bodies banned Qatari planes from landing in the kingdom's airports and banned them from crossing their airspace.
Saudi Arabia accused Qatar of backing militant groups and broadcasting their ideology, an apparent reference to Qatar's influential state-owned satellite channel al Jazeera. According to Saudi Arabia's state media, they decided to shut local Al Jazeera offices following a row.
"(Qatar) embraces multiple terrorist and sectarian groups aimed at disturbing stability in the region, including the Muslim Brotherhood, ISIS (Islamic State—ed) and al-Qaeda," Saudi state news agency SPA said.
It accused Qatar of supporting what it described as Iranian-backed militants in its restive and largely Shiite Muslim-populated Eastern region of Qatif and in Bahrain. Qatar was also expelled from the Saudi-led coalition fighting a war in Yemen.
Qatar denied it was interfering in the affairs of others.
"The campaign of incitement is based on lies that had reached the level of complete fabrications," the Qatari foreign ministry said in a statement.
Iran called for dialogue. Foreign Minister Javad Zarif tweeted: "Neighbors are permanent; geography can't be changed. Coercion is never the solution. Dialogue is imperative, especially during blessed Ramadan."
US Secretary of State Rex Tillerson told Washington has encouraged its Gulf allies to resolve their differences.
A split between Doha and its closest allies can have repercussions around the Middle East, where Gulf states have used their financial and political power to influence events in Libya, Egypt, Syria, Iraq and Yemen.
Regional powerhouse Turkey, an ally of both the Muslim Brotherhood and Qatar, urged dialogue to resolve the spat.
But the economic fallout loomed, as Abu Dhabi's state-owned Ethihad Airways, Dubai's Emirates Airline and budget carriers Flydubai and Air Arabia said they would suspend all flights to and from Doha from Tuesday morning until further notice.
Qatar Airways said on its official website it had suspended all flights to Saudi Arabia.
Qatar's stock market index sank 7.5 percent with some of the market's top blue chips hardest hit.
Some Egyptian banks said they were halting dealing with Qatari banks.
The measures are more severe than during a previous eight-month rift in 2014, when Saudi Arabia, Bahrain and the UAE withdrew their ambassadors from Doha, again alleging Qatari support for militant groups. At that time, travel links were maintained and Qataris were not expelled.
Kristian Ulrichsen, a Gulf expert at the US-based Baker Institute, said if Qatar's land borders and air space were closed for any length of time "it would wreak havoc on the timeline and delivery" of the World Cup.
Football authorities said they were in contact with Qatar.
"It seems that the Saudis and Emiratis feel emboldened by the alignment of their regional interests—toward Iran and Islamism—with the Trump administration," Ulrichsen said.
Qatar used its media and political clout to support long-repressed Islamists during the 2011 pro-democracy "Arab Spring" uprisings in several Arab countries.
Muslim Brotherhood groups allied to Doha are now mostly on the backfoot in the region, especially after a 2013 military takeover in Egypt ousted the elected Islamist president.
The former army chief and now president, Abdel Fattah al-Sisi, along with the new government's allies in Saudi Arabia and the UAE, blacklist the Brotherhood as a terrorist organisation.
Egypt, the Arab world's most populous nation, said on its state news agency that Qatar's policy "threatens Arab national security and sows the seeds of strife and division within Arab societies according to a deliberate plan aimed at the unity and interests of the Arab nation."
Oil prices rose after the moves against Qatar, which is the biggest supplier of liquefied natural gas (LNG) and a major seller of condensate - a low-density liquid fuel and refining product derived from natural gas.
Defense Minister Avigdor Lieberman responded after the Qatar crisis that "even in the Arab countries they understand that the danger is not Zionism but terrorism." Lieberman added that "their fear is of radical Islamic terrorism, and there is no doubt that this opens the possibility of cooperation in the fight against terrorism."
Russian Foreign Minister Sergei Lavrov, in a phone conservation with his Qatari counterpart Sheikh Mohammed bin Abdulrahman al-Thani on Monday, called for a resolution to differences between Qatar and other Arab countries through talks, the ministry said.