He said six children had been rescued from the rubble.
Local residents said as many as 35 people could have been inside the building when it collapsed.
The victims were said to be aged between five and 12 years.
Soldiers were deployed to help with the rescue.
Heavy rains have caused mudslides at several places in Uttrakhand state this week.
"There has been separate incidents of house collapsing in Uttrakhand because of the heavy rains," Rautela said.
Troops have been rushed to the state to help thousands of Hindus who were stranded near a pilgrimmage site after torrential rains washed away a key bridge on Sunday.
India is experiencing heavy rainfall this monsoon season, which usually continues into October.