The non-combatants escaped Saturday evening from the remaining area under the control of the Liberation Tigers of Tamil Eelam (LTTE), the ministry said in a statement.
"The civilians started arriving in large groups since (Saturday) afternoon using the safe routes opened for them by troops," the ministry said.
The influx into government-held territory was in contrast to the trickle of civilians that came through when the military observed a unilateral two-day truce earlier in the week, the ministry noted.
Security forces kept up their offensive against Tamil Tiger rebels trapped in a government-declared "no-fire zone," ignoring international appeals for a ceasefire.
At least 17 rebels were killed and another 22 wounded in fighting Saturday, the government said.
"Battlefield reports indicated that troops have encountered stiff resistance from the terrorists," it said.
President Mahinda Rajapakse told party workers at his tightly guarded residence in Colombo Saturda