The event reportedly cost almost $800,000 (£575,000).
The opposition Movement for Democratic Change (MDC) called the celebrations “obscene”.
Mr Mugabe has dominated Zimbabwe politics since independence from the UK in 1980.
The event, which was televised and featured schoolchildren reading poetry about the president, was held in the drought-stricken south eastern city of Masvingo.
The elderly leader, accompanied by his wife Grace, released 92 balloons to kick off the event at the Great Zimbabwe monument, with tens of thousands of people attending.
In a speech, Mr Mugabe attacked Western donors, and said he would not accept “rotten, filthy” aid if it was contingent on Zimbabwe accepting same-sex marriages, the government-owned newspaper the Herald reported.
But the opposition Movement for Democratic Change (MDC) said the celebrations were “ill-conceived”.
Money used for the event should be used to import maize “to avert the impending starvation” in Masvingo and other areas, said Obert Gutu, a MDC spokesman.
Eddie Cross, an MP for the MDC said: “The obscenity of this particular exercise is that he throws this bash not just based on public funds… but he does it in one of the worst-affected drought-stricken parts of the country.”
The UN’s World Food Programme said food production had fallen by half compared to a year earlier, because of severe drought.
The government said about three million people were food insecure and earlier this month it asked for nearly $1.6 billion in aid.
Mr Gutu said the ruling Zanu-PF “should be utterly ashamed” for hosting the costly celebration while “more than 90 %of Zimbabweans are wallowing in grinding poverty”.
However, a youth leader for the ruling Zanu-PF party defended the birthday celebrations.
“Money is not the issue here,” Pupurai Togarepi told the Reuters news agency.
“You cannot put a price on the contribution of President Mugabe to the history and development of this nation. All these things are worth more than money.”
Zimbabwe has faced severe economic challenges in recent years, which critics blame on policies including the seizures and redistribution of white-owned farms in 2000.
Hyper-inflation left its currency worthless and required the use of foreign currencies for most transactions.
Mr Mugabe has blamed his country’s economic troubles on Western meddling.
Veteran leader Robert Mugabe has presided over Zimbabwe for the past three decades.
Born in 1924 in the village of Kutama, south-west of the capital Harare, he was educated by Jesuits and went on to become a teacher before joining the liberation struggle against British rule.
He became a key figure in the fight for independence from white minority-rule as leader of the Zimbabwe African National Union, and spent 11 years in prison before becoming Zimbabwe’s first post-independence prime minister in 1980.
In December 2015, Mr Mugabe was endorsed once more as the ruling party candidate for the 2018 presidential elections but media continue to speculate about a potential successor.