Egypt had earlier invited President Hassan Rouhani to attend the ceremony.
Sisi has been sworn-in as the new president at Cairo's Constitutional Court amid high security.
The ceremony was followed by a reception at Cairo's Ittihadiya presidential palace.
At Ittihadiya palace, the Iranian deputy foreign minister held a meeting with Egyt's new president and wished him successs.
Sisi was declared the country's president last week after winning 96.6 percent of the presidential vote, beating the only other contender Hamdeen Sabahi.
Turnout was recorded at 47 percent, lower than Sisi had called for, and despite the voting period being extended from two to three days. Sabahi won 3.09 percent of the vote.
He replaces the outgoing interim president, Adly Mansour, who returns to his post as chief justice of the Supreme Constitutional Court.