The ministry said the two-storey-deep bunker had electricity generators, air conditioning and medical supplies, and was hidden in a coconut plantation in Mullaittivu district.
There was no sign of the Liberation Tigers of Tamil Eelam (LTTE) leader, Velupillai Prabhakaran.
"Sri Lankan army troops... have captured a main LTTE hideout, what is believed to be a major residential site of the terror leader Prabhakaran," the ministry said.
It said the facility fell during fighting on Monday, and that at least 20 rebels died trying to defend it.
The whereabouts of Prabhakaran, 54, are not known, but Sri Lanka's military has said the Tiger supremo could may have already fled the island by boat.
A massive government offensive has seen the LTTE's territory shrink from some 18,000 square kilometres (7,000 square miles) a year ago to an area of less than 300 square kilometres (110 square miles) now.
The government says it is on the brink of total victory against the rebels, who are fight