Mubarak, 82, has been in power for 29 years and had gall bladder surgery at Heidelberg University Hospital in Germany in March. Mosques across Egypt were instructed by the government to pray for the president's health.
The president's aides gave no reason for Mubarak's cancellation of this trip to Kampala, Uganda, for the AU summit. Prime Minister Ahmed Nazif is to attend.
Mubarak has periodically canceled meetings in the past several months but has also been in the public eye most weeks.
Even though doctors in Germany gave him a clean bill of health, worries have persisted. These appeared allayed last week when Mubarak appeared on television for 10 minutes to give a national address. He appeared strong, but thinner than usual, as he spoke on the eve of the annual Revolution Day to commemorate the military coup that toppled the monarchy in 1952.
During his television address he said economic growth and social justice are the main political goals and he also urged all politicians to work toward attaining them.
"While I look forward to parliamentary elections that push forward our democratic experience, I call on all political parties to come up with ideas and visions to deal with these priorities, on which there is no disagreement," Mubarak said.
The country will have elections in October for its 454-seat lower house. The last elections were in 2005 when the National Democratic Party took more than 310 seats.
Mubarak, a former Spitefire pilot in the Egyptian air force, is the fourth president of Egypt. He was appointed vice president in 1975, and became president in October 1981 immediately after the assassination of President Anwar Sadat.
Mubarak ends his fifth 6-year term next year and he hasn't stated whether he run for a sixth term.
As Mubarak ages amid health concerns, the population speculates about his successor. It is widely thought that he is grooming his banker son Gamal, 46, who is considered a market modernizer and who heads up the policy committee of the National Democratic Party.
Jimmy, as Gamal is affectionately called, studied at the American University in Cairo and was 11 years at Bank of America in Cairo and London.
While Egypt has moved toward a more market-oriented economy under Mubarak, there is impatience among the rural population who say they have yet to benefit from increased national wealth. Around one-fifth of Egypt's 78 million people live on less than $1 a day.
This could make Gamal's road to the presidency a bumpy one if he is associated too much with his father's policies.
The main opposition -- and banned -- left-of-center Muslim Brotherhood, which took one-fifth of the parliamentary seats in 2005 presidential elections, says Gamal isn't liked by the people.
"He has no popularity at all and I don't think he has the ability to control such a big country," Brotherhood's spokesman Essam al-Erian said.
Another possible contender in a presidential election is Egypt's powerful intelligence director, Omar Suleiman, 72. He is said to be well regarded by the Israelis and Palestinians for his attempts to mediate peace deals.
Many people are also waiting for firmer International Atomic Energy Agency head Mohamed ElBaradei to declare his political intentions. ElBaradei returned to Egypt last year and is said to be assessing the political climate. He' only said he wants to be an agent of change for Egypt.