The incident took place at Manikaran in Kullu district of the state, said Deputy Commissioner Rakesh Kanwar in Kullu.
A mound of stones and debris from the hill atop the eight-story residential complex got dislodged due to recent heavy rains and struck the temple at around 2:00 p.m. local time (0830 GMT), damaging part of the residential area of the temple, he said.