Egypt accuses Hamas of supporting militant groups seeking to topple the Cairo government, an allegation the movement denies.
Hamas warned in a statement that the abductions could strain ties with Egypt, which faces a serious security challenge from Islamist militants.
"The graveness of such an incident was that it was the first of its kind and it breaks all diplomatic and security norms of the state of Egypt," said the group, which called on the authorities to quickly apprehend the kidnappers.
A bus with about fifty Palestinians on it was travelling from Rafah on the Egypt-Gaza border to Cairo airport when it was ambushed, the security sources said.
Hamas' interior ministry confirmed that four Palestinians were kidnapped on their way to Cairo.
"We urge the Egyptian interior ministry to secure the lives of the kidnapped passengers and free them," Gaza interior ministry spokesman Eyad al-Bazom said, adding that the bus was being escorted by Egyptian soldiers.
Spokesmen for Egypt's military and interior ministry could not be reached for comment.
No group has claimed responsibility for the incident.
Hamas has long had ties to the Egyptian Muslim Brotherhood that was ousted from power when former president Mohamed Mursi was overthrown by the army in 2013 after mass protests against his rule.
The Egyptian government has accused Hamas of helping Islamist militants in Egypt's Sinai desert, which borders on Gaza, to attack its security forces. Hamas denies this.
A decision by an Egyptian court in June to cancel a previous ruling labelling Hamas a terrorist group raised speculation that relations between Egypt and Hamas may improve.
Sinai is the focal point of an Islamist insurgency that aims to overthrow the government, and the most active militant group in the area is the Egyptian affiliate of Islamic State, Sinai Province.
The insurgency has killed hundreds of policemen and soldiers and Sinai Province recently killed an abducted Croatian hostage.