President Hery Rajaonarimampianina said it was a "terrorist act", and blamed it on "political divergences".
The situation remains fragile in the country, with supporters and opponents of the president at loggerheads.
The blast happened during a free concert at the Mahamasina stadium. A military parade had been held there earlier.
It was not immediately clear who or what was behind the explosion.
In a statement broadcast on national television, the president said: "Divergences in point of view may exist between us... [But] if the leader does not suit you... you cannot kill the population," he said.
"We will never tolerate destabilisation. Especially because this is not only destabilisation but an act of terrorism."
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