The ban was announced as Mugabe, who has ruled Zimbabwe since independence from Britain in 1980, turned 83 on Wednesday.
Police in Harare published notices saying there had been "pandemonium, looting and destruction of property" following opposition political rallies in some townships this month, which warranted a temporary ban until May.
"The holding of rallies and demonstrations in Mbare district [and Harare South] are prohibited from today 20th February 2007 to 20th May 2007; that is, a period of three months," police officials said in a statement.
Al Jazeera's Haru Mutasa, who was present at Mugabe's birthday celebrations at his Harare home, said although the president could forget the economic challenges facing his country for a few hours, they appeared to keep piling up.
She said Zimbabwe owes the International Monetary Fund money – foreign currency the country doesn't have - and prices of basic food commodities keep going up and civil servants are threatening mass action.
Mutasa said: "Bread makers have stopped making bread because the cost of baking it is far too expensive.
"So as the president celebrates his 83rd birthday, Zimbabweans are bracing themselves for another food shortage."
Nelson Chamisa, the MDC spokesperson, said the ban on protests showed Mugabe was unsettled by growing anger over a crumbling economy largely blamed on his politically driven policies.
"It is clear the regime is panicking. They are trying to impose a state of emergency ... this is tantamount to banning the MDC and all political activity," said Chamisa, vowing to continue "to organise our meetings and rallies where necessary".
Police on Wednesday continued to patrol some poor townships and the city centre, a show of force analysts said was meant to pre-empt any action by the opposition.
Zimbabwe has, since the start of the year, witnessed a spate of industrial strikes for higher wages, including by doctors and some teachers, and unions are threatening more job boycotts, which the authorities fear could spill onto the streets.
Mugabe denies running down the economy and says his government is a victim of a Western sabotage campaign over his policy of seizing land from white farmers to resettle blacks.
Mugabe, who remains defiant in the face of the damaging economic crisis, denied opposition charges that he wanted to hang on to power after the end of his current term next year.