The defender didn’t appear to make contact with Coman and Kovac told media after the game that they would need to wait for tests to see the severity of the injury.
Bayern have since revealed the injury to be to a tear to Coman's hamstring, and that the club expect him to miss significant time.
"Kingsley Coman will not be available for Bayern Munich for now," read a club statement. "The French winger has suffered a torn muscle fibre in his left posterior thigh this Saturday afternoon during the Bundesliga home game against Hertha
"This is the result of the tests conducted by Bayern's medical staff."
Coman's first knock against Augsburg eight days ago left him a concern for Tuesday’s Champions League tie against Liverpool, but the 22-year-old recovered sufficiently to start the first leg at Anfield before being replaced in the final 10 minutes by Frank Ribery.
The French winger has suffered recurring injuries to the same ankle during the last 12 months with the Bundesliga champions.
He required surgery for the injury last season, which ultimately ruled him out for France for the 2018 World Cup as well as much of Bayern's title-winning season.
Returning to start the Bundesliga season, Coman went down with the same injury in this year's league opener, requiring another surgery and sidelining him until December.
He had previously said in December he would consider retirement if his ankle problems continued, though Bayern chief Karl-Heinz Rummenigge has since publicly discouraged him from considering that option.
Against Hertha, Javier Martinez’s 63rd-minute goal was enough to seal a nervous win and drag last season’s champions level on points with league-leaders Borussia Dortmund.
Martinez headed home from a corner with half an hour to play to shatter the visitors’ resistance and keep Bayern in touch with their rivals at the top.
The champions now sit second in the Bundesliga on goal difference, but will see the gap stretch back to three points if Dortmund beat Bayer Leverkusen on Sunday.
Hertha’s Karim Rekik was red carded late on as the visitors finished with 10 men at the Allianz Arena, with Bayern holding on to keep their first clean sheet in the league since the turn of the year.