The stadium, completed less than six years ago, is currently the city's main football venue while the Maracana is rebuilt for this year's Confederations Cup and the 2014 World Cup.
"Today, they informed me that the roof has structural problems," Eduardo Paes said.
"I asked if this represented a risk for spectators and they told me it did, depending on the wind speed and temperature."
"On that basis, I immediately decided to close the stadium until we had more details.
"It's simply not acceptable that a stadium which was inaugurated such a short time ago now has to face this sort of situation."
The first event to be affected was Wednesday's Carioca championship match between Brazilian champions Fluminense and Macae.
Although the Joao Havelange stadium will host the athletics in 2016, the opening and closing ceremonies will both take place at the Maracana.
The stadium was built for the 2007 Panamerican Games at a cost of 380 million reais and opened just one month before the event. Afterwards, it was leased to local football club Botafogo although it is frequently used by other teams.
The capacity of 46,000 will be increased to 60,000 for the Olympics.
The Maracana is due to re-open at the end of April, four months behind the original schedule.
- Sports & Recreation