Bhandari, 25, who has played two One-day Internationals, will be available for the last two matches of the ongoing Limited Overs series at Lahore on March 21 and 24.
Nehra received two stitches when he split the webbing of his bowling hand while fielding during the second One-dayer at Rawalpindi on Tuesday and was ruled out for at least two weeks.
"Nehra is returning home as soon as possible for further treatment," team official Amrit Mathur said on Wednesday. It is unlikely the left-arm seamer will be considered for the three-Test series starting on March 28.
Nehra was supposed to have missed Tuesday's play as well after an old ankle injury flared up again on the eve of the match and the team management declared his unavailability for the game.
But the bowler, whose spot-on final over won India the first One-dayer at Karachi on Saturday, was surprisingly retained in the team and finished with 3-44 in Pakistan's total of 329 for six.
Pakistan won the match by 12 runs to level the five-match series 1-1. The third One-dayer will be played in the northwestern city of Peshawar on Friday.
Bhandari, Nehra's Delhi team-mate, made his debut against Pakistan at the Asia Cup in Bangladesh in 2000 and was discarded after being smashed for 2-75. He was recalled for one match during the recent tri-series in Australia and fared better by picking up 3-31 against Zimbabwe at Perth.
India are already without three injured frontline bowlers, seamer Ajit Agarkar and spinners Anil Kumble and Harbhajan Singh, on their first full tour of Pakistan since 1989.