The group had cleared a section of jungle north of the Trincomalee district and had begun building an airstrip, the ministry said on Thursday.
"The operation was conducted to prevent the construction of this unauthorised air facility, which poses a grave security threat not only to the sovereignty of Sri Lanka but the entire region," the ministry said in a statement.
The attack was the second in two days after the Sri Lankan military bombed Tamil areas on Wednesday in attempt to end a water supply blockade.
The government accuses the Tigers of blocking water supplies to farmland in the eastern district of Trincomalee, where the government and rebels both control territory.
The Tigers say local Tamil civilians stopped water flowing from a reservoir, demanding that the government build water towers in Tamil areas.
A government official said ground troops were also preparing to enter the area to end the blockade.
"Ground troops are moving with engineers to the area. If they call for air suppport, then air support will arrive," said Keheliya Rambukwella, a defence ministry spokesman.
The bombing raid is the latest in a series of attacks and clashes between the military and the Tigers that many fear could end a 2002 ceasefire and re-ignite a war that has killed more than 65,000 people since 1983.