"There are two dead and 26 injured," Jean Claude Razafimahandry, a hospital director, told AFP.
He said the rush was caused by "overcrowding at the entrance of the Mahamasina stadium" in the capital Antananarivo.
The dead were a male teenager and a woman in her fifties.
Madagascar, which recently returned to democracy following a coup in 2009, was celebrating 54 years since its independence from France.
The US State Department said in statement earlier in the day that "this year's anniversary carries special significance as the first since Madagascar's return to democratic rule."