Farid el-Deeb, a lawyer for Mubarak, made the claim just two weeks before the former Egyptian president wa expected to go to trial to face charges he ordered the killings of protestors back in February.
The 18-day uprising resulted in him being ousted from office. A conviction could carry the death penalty.
Activists suspect his lawyer may be using health problems as a way to sway public opinion.
State TV dubbed the new government lineup the "Revolution Cabinet." Most of the newly appointed ministers were relative newcomers, clearly a way to avoid further criticism by the protesters.
Thousands of Egyptians have returned to Tahrir Square, the epicenter of Egypt's uprising, complaining that change has come too slow under the military council that took over power.
Even after the Cabinet reorganization, many of the protesters in the square said they have no intention of quitting more than a week into their sit-in.
The most prominent among those replaced is Antiquities chief Zahi Hawass. For more than a decade, he has been the international face of Egypt's archaeology, with his trademark "Indiana Jones" hat that turned him into an instantly recognizable global icon. Hawass, however, has been the target of a series of heavily publicized protests by archaeology graduates who accused him of corruption and seeking publicity for himself.
He has been accused of being too close to Mubarak and his family, along with former culture minister Farouq Hosni, himself a Mubarak protege who had served in the Cabinet for 25 years until he was pushed out after the revolution.
In 2010, Mubarak was treated for cancer in his gallbladder and pancreas. El-Deeb said in June that the former leader may be suffering a recurrence that spread to his stomach. However, two senior Egyptian medical officials - one of them the head of Mubarak's team of doctors - said at the time he did not have the disease.
Mubarak's purported health problems have complicated efforts to bring him to trial. He was hospitalized on the day prosecutors sought to question him for the first time.
Prosecutors have questioned him in the hospital, but an order to transfer him to a Cairo prison during the investigation was overturned on the grounds that the prison health facilities were inadequate to treat him. A report by a government-appointed panel of physicians determined in May that Mubarak is too ill to be held in prison while awaiting trial.
Mubarak's sons, Alaa and Gamal, have been held in Cairo's Tora prison since mid-April while they are investigated on charges ranging from corruption and squandering public funds to ordering the violent suppression of anti-government demonstrations.
The Associated Press contributed to this report.