The Germany international strained adductor muscles late in the 2-1 defeat by Zenit St Petersburg on Wednesday that saw Dortmund advance to the Champions League quarter-finals with a 5-4 aggregate win.
Schmelzer is set to miss miss both last-eight ties in April and could also be out for the first leg of the semi-finals if his team progress.
Dortmund, battling to hold on to second place in the Bundesliga, already have Germany internationals Ilkay Guendogan and Sven Bender sidelined as well as central defender Neven Subotic and midfielder Jakub Blaszczykowski.
Midfielder Marco Reus was also absent for Wednesday's game but is expected to return at Hanover 96 on Saturday. (Reporting by Karolos Grohmann, editing by Tony Jimenez)