Kohli, who fell for a duck during a rush of early wickets before India recovered to post 227 for six, sustained his blow while bowling as the home side fought in vain to avoid defeat.
The occasional medium-pacer hurt his knee in a fall when his back foot slipped as he came in to bowl and he had to limp from the field.
The Board of Control for Cricket in India provided an update on his fitness, with the news boding well for Kohli as no serious damage was detected in a scan.
A statement from the BCCI's honorary secretary Sanjay Jagdale read: "Virat Kohli, who sustained a foot injury while bowling in the first AIRTEL ODI against Pakistan at Chennai earlier today, underwent an MRI scan after the game.
"All his major ligaments are fine. There is minimal injury fluid in his knee. He will recover after treatment."
The statement on the BCCI website added: "His condition will be monitored, and a decision on whether he will play the second AIRTEL ODI at Kolkata on 3 January 2013, will be taken over the next couple of days."
Pakistan claimed a six-wicket win in Chennai to take a 1-0 lead in the three-match series.