The hospital in Mannar district was partially damaged by heavy artillery from the Liberation Tigers of Tamil Eelam (LTTE), the defence ministry said, adding that a few shells had also fallen close to a nearby state-run school.
"The explosions had caused panic and trauma among patients and civilians who were immediately evacuated by troops into safer shelters," the ministry said in a statement.
It was not immediately clear if there were casualties.
Meanwhile, security forces killed at least 35 rebels in fighting in the north on Monday, the ministry said, placing its own losses at six soldiers wounded.
There was no immediate comment from the Tigers, whose armed struggle since 1972 for an independent state for minority Tamils in the majority Sinhalese nation has left more than 60,000 dead.
At least 2,508 rebels have been killed since January, while 151 soldiers have lost their lives in the same period, according to defence ministry data.
Casualty numbers given by both sides can