Talaat Sadat, who was also convicted of spreading disinformation, was taken into custody immediately after the verdict was announced on Tuesday, his brother Mohammed-Anwar Sadat said.
He was also fined 200 Egyptian pounds ($35).
Sadat, an opposition politician, was put on trial for saying that the 1981 assassination of President Sadat was an international conspiracy in which senior Egyptian military officials at the time were involved.
An Islamist militant shot the former president dead as he watched a military parade.
The gunman was tried and executed.
"We do not know what to do now ... The verdict was a surprise to all of his lawyers," the legislator's brother told Reuters.
There is usually no appeal against emergency military court verdicts, although convicts can ask President Hosni Mubarak for a pardon.
President Sadat was assassinated during a military parade in 1981
Egypt's parliament speaker agreed to strip Talaat Sadat's parliamentary immunity after a request from military prosecutors earlier this month following his remarks about Sadat's assassination.
Sadat has said his comments were not intended to insult the military establishment, and later published newspaper advertisements professing respect for the army.
Several Egyptian human rights organisations have said the decision to put Sadat on trial before a military court was a violation of the right to free speech.
Sadat is a member of the small opposition party, Al-Ahrar.