An air force spokesman said two Mi-24 helicopter gunships were damaged in the Tiger attack.
At least eight air force troops have been wounded in the attack.
The spokesman said troops had launched a clearing operation after the Tiger attack.
In a separate incident an air force Bell 212 aircraft made a forced landing in Mihintale, to the east of Anuradhapura, killing the two pilots and two door gunners.
Air force officials said it was not known how the helicopter crashed.
The air force base at Anuradhapura, 212 kilometres (130 miles) north of the capital Colombo, came under attack and "heavy explosions and firing of weapons" were heard, the French new agency AFP reported quoting a defence ministry statement.
AFP quoted local residents as saying gunfire was heard in the area, while military officials said the army base had been on alert before the attack.
The Defence Ministry statement said the Air Force base at Anuradhapura came under "terrorist attack" at 3 a.m Monda