Gaza security sources told AFP that Mahmud Zahar, Khalil al-Haya, Imad al-Alami and Nizar Awadallah passed through the southern Gaza Rafah terminal, the only crossing point with the enclave not controlled by Israel.
They were heading to Cairo for talks with intelligence chiefs on relations between the sides.
Former army chief Abdel Fattah al-Sisi, who deposed Morsi, won presidential elections in 2014 on a pledge to wipe out Islamist militants.
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The militant Islamic Hamas, which rules Gaza, has its origins in the Muslim Brotherhood movement which is outlawed in Egypt.
On Sunday, Egypt's Interior Minister Magdy Abdel Ghaffar said both organisations were involved in last year's assassination of the country's top prosecutor.
Since taking office, the Sisi government has accused Hamas of aiding jihadist groups in the Sinai Peninsula who have repeatedly attacked Egyptian security forces.
Egypt has largely kept its border with Gaza closed since 2013 and has destroyed hundreds of Palestinian tunnels under the frontier used to smuggle commercial goods, cash, people and, allegedly, weapons.