Blaszczykowski picked up the problem in Dortmund's 1-1 draw at Hannover last weekend, with the club's medical team predicting a spell of six weeks on the sidelines for the winger.
The Poland captain told Bild that he wants to make a speedy recovery to help both club and country over the autumn.
He said: "I immediately felt something wrong. As an athlete, you notice this.
"It's not easy, especially since I've had a good season. But I've had worse things. I will fight and try to come back quickly.
"This is very annoying. But it cannot be helped. The guys can do it without me."
The 26-year-old will miss Poland's home World Cup qualifier against England next week, but revealed that he plans to attend the game to support his side.