The fire started late on Wednesday at the home in Anguruwatota town.
Fifty-one residents were rescued, police spokesman Fredrick Wootler said.
People with mental illnesses were also housed there, he said.
The director of the home was arrested on suspicion of causing deaths through negligence.
Associated Press footage showed the building gutted with its charred furniture and equipment, with bodies lying nearby.
Local television channel Hiru showed image of firefighters, police and residents trying to contain the raging fire.
Those rescued were assisted by police and soldiers in boarding buses to a safe location.
Chathura Mihudum, director of the National Secretariat for Elders, said the facility was not registered as a nursing home and had been warned to follow laws and guidelines.
He said it was overcrowded with beds for just about 15 people in a space where 71 people were living.
Government officials had previously visited the institution and had instructed the management to follow laws, he said, without elaborating.
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