The blaze broke out about 5:30am [23:30 GMT] and quickly spread through the single-storey Soviet-era building.
Locked doors and barred windows were said to have trapped some of the victims inside the building.
Robin Forestier-Walker, Al Jazeera's correspondent in Kazakhstan, said a patient had confirmed to him that "they had been locked in and weren't able to escape".
"The wife of a man who had been killed had been told the same thing by medical staff there," he said.
About 40 people were evacuated from the building, emergency officials said.
Violations of safety regulations are common across the former Soviet state and fatal fires are frequent.
There have been almost 10,000 fires in Kazakhstan in the first eight months of 2009, according to government statistics.