Doctor Tango Oscar Toky, chief physician of the Ikongo hospital, said "nine people died on the spot" and another five died later in hospital.
Nine of those injured were in a critical condition, he said.
"The gendarmes... fired on the crowd," Jean-Brunelle Razafintsiandraofa, a lawmaker in the southeastern town of Ikongo told AFP.
Razafintsiandraofa said an angry crowd gathered outside the local police station demanding officers release four kidnapping suspects arrested on Sunday, so they could be dealt with by the mob.
Around 500 protesters armed with blades and machetes "tried to force their way" into the station, a police officer involved in the shooting told AFP, speaking on condition of anonymity.
"There were negotiations, the villagers insisted," the officer said over the phone, adding police fired smoke grenades and shots in the air in an attempt to disperse the crowd.
"They continued to force their way through... We had no choice but to defend ourselves," the police officer said.
Some sub-Saharan African countries have suffered a wave of assaults against people with albinism, whose body parts are sought for witchcraft practices in the mistaken belief that they bring luck and wealth.
The kidnapping took place last week, according to Razafintsiandraofa, an MP for the Ikongo district about 90 kilometers southeast of the capital Antananarivo.
No further details were immediately available.