A scan on Sunday on the left-back’s right ankle revealed the injury after Schmelzer was stretchered off with half an hour gone of Saturday’s goalless draw at Freiburg.
The 29-year-old Germany international is expected to miss the next seven weeks having only returned on Saturday from tearing ligaments in the same ankle last July.
Freiburg’s Yoric Ravet, who had initially been booked for the tackle, was sent off for the foul on Schmelzer after the video assistant referee spotted the midfielder had gone in studs up.
The VAR is being trialled in Germany this season and this was the first time an intervention led to a player being sent off.
“I knew straight away that I wouldn’t be able to continue,” said Schmelzer before the diagnosis.
“I don’t blame him (Ravet), he wanted to play the ball, that is legitimate and he apologised in the dressing room.”
Dortmund hope Spanish centre-back Marc Bartra, who went off against Freiburg with a groin injury, will be fit to face Spurs in their opening Champions League group match.
His club has not ruled him out of the Wembley encounter.