The Germany international faces a four-week lay-off after picking up the injury during his side's 2-1 defeat to Zenit St Petersburg on Wednesday.
That result was still enough for the Westphalians to complete a 5-4 aggregate win to join Bundesliga rivals Bayern Munich, the side who beat them in last season's Champions League final, in the last eight.
In spite of his injury, Schmelzer was nonetheless relieved Dortmund made it through after they encountered more difficulty than they might have imagined at the Westfalenstadion.
"Definitely I'm delighted we've made it through," he said on his club's website. "We are once again among the best eight sides in Europe, and that's amazing.
"It was a tough game and Zenit played well and made life difficult for us. But in the end, all that matters is we're in the next round."
Although he will not be involved in either leg of the quarter-finals, Schmelzer is looking forward to Friday's draw, hoping it is favourable to his team-mates to enable him potentially to return for the semi-finals.
"There are a few teams in there we've not met yet and so it would be nice to play against a side who we don't know yet," he said.
"But we can't change or have any influence on the draw. We've just got to give it our best shot. Anything's possible in the next round."