Tahir sustained the injury to his left hand during his side`s six-run defeat against England in Chennai on March 6.
"It was a chipped fracture. Scans have been sent back to South Africa and the period of recovery recommended is for 10 days. Imran bowled in the nets this morning and he`s fine because the injury is not on the bowling hand.
"The selectors will decide when the 10-day period starts, whether it starts now or after the game against India. Imran is pretty much part of the World Cup squad," South African team manager Mohammed Moosajee told reporters here today.
The Pakistan-born 31-year-old spinner has been a revelation in the World Cup so far, taking 11 wickets in three matches, the highest by a South African in the tournament. He is behind Pakistan skipper Shahid Afridi, who has 15 wickets from four matches.
Asked specifically whether Tahir will play the match against India, Moosajee said, "As of now he is available for selection. It`s entirely on the selectors to take a call when to give him the rest. It may be decided on the day of the match."
South Africa are likely to name off-spinner Johan Botha as replacement if Tahir misses the match against India.
The Proteas` last two matches at group stage are against Ireland on March 15 and Bangladesh on March 19 while the knock-out stage begins from March 23.
Tahir made his international debut in this World Cup after qualifying to play for his adopted country through marriage in January.