The blasts took place over several hours at the Gongola Mboto military base.
A military spokesman said casualties were possible but officials would not know until daylight on Thursday.
The city’s airport was reported to have been closed after the blasts, the British foreign office said.
Residents were encouraged to stay inside their homes and away from windows after the explosions, which hurled debris across the city.
“Of course there might be injuries and deaths but it’s not yet confirmed,” military spokesman Lt Col Kapambala Mgawe Mgawe said.
“We are not allowed to go closer and, of course, the road to Gongola Mboto has been closed.”
The British foreign office said the police had set up an evacuation centre accepting those within a 10km from the explosion site.
Explosions at an ammunition depot at Mbagala army base in spring 2009 killed at least three people.
There is currently disruption to flights in and out of Dar es Salaam International Airport.
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