Mr Meles was admitted to hospital in July. The nature of his condition has not been made public.
Speculation about his health began when he missed an African Union summit in Addis Ababa earlier last month.
Mr Meles took power as the leader of rebels that ousted communist leader Mengistu Haile Mariam in 1991.
Deputy Prime Minister Hailemariam Desalegn, who is also Ethiopia’s foreign minister, will be acting head of government, state television said.
“Even if Ethiopia has been badly affected for missing its great leader, Prime Minister Meles Zenawi initiated fundamental policies and strategies which will be further strengthened,” the TV said.
Three weeks ago, a government spokesman told the BBC that Mr Meles was in “a good condition and recuperating”, and dismissed reports he was critically ill.
The spokesman, Bereket Simon, declined to give any details about Mr Meles’ whereabouts or what he was suffering from.
At the time, there were reports that Mr Meles was in hospital in Belgium, suffering from a stomach complaint.