Head coach Niko Kovac said after the match: "We hope that it's not too bad and that he'll be back in the next few days."
Bayern confirmed on Thursday that Coman "only suffered a badly bruised knee" and is expected to return to training on Friday.
Bayern were beaten on penalties after a 2-2 draw with Spurs in their final pre-season fixture, with Jann-Fiete Arp and Alphonso Davies on the scoresheet.
They had been two goals behind after goals from Erik Lamela and Christian Eriksen, but their comeback wasn't enough as Spurs scored all of their penalties in a 6-5 shoot-out win.
They now face Dortmund at Signal Iduna Park in the traditional season curtain-raiser, with Dortmund having finished second in last season's Bundesliga.
Dortmund had for some time looked like ending Bayern's hegemony in the league but Kovac and his side turned things around in the second half of the campaign, clinching another league and cup double.
After the Supercup, they will begin their defence of the cup with a DFB-Pokal trip to Energie Cottbus on August 12.
While still only 23, Coman is entering his fifth season as a first-team regular at Bayern having initially joined on loan from Juventus back in 2015.
He will be hoping to build on an impressive season on a personal note, having hit ten goals in all competitions for the first time in his senior career.
One of those goals came in the DFB-Pokal final win over RB Leipzig, as Coman scored the second in a 3-0 Bayern win.
Coman is one of the players whose starting spot could be under threat, with the Bavarians strongly linked with moves for left wingers Leroy Sane and Leon Bailey.