The 26-year-old played the whole 90 minutes of Dortmund's 1-0 defeat to Hamburg on Saturday despite breaking bones in his hand during the match.
Dortmund confirmed that Schmelzer had been operated on after the encounter at Signal-Iduna Park and now faces a spell on the injury list.
"Marcel Schmelzer suffered a metacarpal fracture of the right hand in the Bundesliga match against Hamburg on Saturday," team doctor Markus Braun told Dortmund's official website.
"Schmelzer was successfully operated on Saturday night and is expected to be out for four weeks."
The blow caps a frustrating start to the season for the Germany international, who has only been able to make five appearances in all competitions after a groin injury earlier in the campaign.
His absence adds to a growing injury list for coach Jurgen Klopp, the 47-year-old also making do without Marcos Reus, Henrikh Mkhitaryan, Ilkay Gundogan and Jakub Blaszczykowski.
Dortmund have struggled to find their form in the Bundesliga this season, with Saturday's defeat - their fourth in seven matches - leaving them 10 points adrift of leaders Bayern Munich in 13th position.
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