Gamal Hussein Ahmed, a 49-year-old tailor, was arrested in the Egyptian capital. He told his investigators that he was "angry at what is taking place in the Palestinian territories."
Ahmed, a drug addict who had previously been in rehabilitation, was on his way to the American embassy to seek political asylum when police arrested him at 1 am, the ministry said.
The Interior Ministry added in its statement that the suspect had already been arrested in the past as part of an investigation focusing on a radical organization which attacked clubs in Cairo, but was never prosecuted.
In the 1990s, the man was convicted of fraud offenses in Libya and even served three years in prison before being deported back to Egypt.
The incident took place Sunday morning, when a man hurled a suitcase containing a makeshift bomb made of gasoline canisters at Cairo's main downtown synagogue. There were no injuries or damage, police said.
An Egyptian security source said the device was thrown by an unknown person who arrived at the Panorama Hotel, which is located across the street from the synagogue.
The Shaare Shamayim Synagogue is not in everyday use, and holds most of its events on holidays, when it is attended by Cairo's Jews, workers of the Israeli Embassy, American students studying in the Egyptian capital and others.
AFP and The Associated Press contributed to this report