The Nigerian had to be replaced 35 minutes into the encounter, having fallen to the ground in pain and clutching his hamstring after over-stretching in an attempt to win the ball.
The club has now confirmed the 31-year-old’s prognosis following a medical scan.
“He had his scan, and is expected to be out for three weeks,” said the club’s media officer Julian Bailey.
Obinna has been City’s first-choice attacker in recent matches, featuring in eight matches since joining in September, with his opening strike in the derby win over Ajax Cape Town his only goal.
Coach Benni McCarthy lamented the striker’s setback, but hopes it will only be a temporary lay-off for the former West Ham United and Inter Milan forward.
“It’s frustrating seeing someone work so hard and put in massive effort to be there, and then something silly where he first sprinted and felt something, before then stretching for the ball and feeling it the second time,” McCarthy said.
“I hope it’s just age catching up, and nothing major.”
Following their exit in the first round of this year’s Telkom Knockout, and with the FIFA international break upon us next week, City are only in action next against Baroka FC on November 22.