Kirilenko suffered the injury in the second quarter of Sunday night's victory over the Dallas Mavericks, left the game shortly thereafter and did not return.
X-rays taken of his ankle were negative.
It was the 32nd game of the season that Kirilenko has missed due to injury.
He missed 25 straight games earlier in the season due to back spasms.
Kirilenko, 33, is averaging 5.2 points and 3.2 rebounds for the Nets this season.
The Nets announced at halftime that reserve guard Marcus Thornton would be out for the rest of the game with a bruised lower back.