The Armenia international limped out of Saturday's 1-0 defeat to Hertha Berlin with the scores goalless, having initially impressed in midfield.
Mkhitaryan's replacement, Jakub Blaszczykowski, coughed up possession for Julian Schieber's winner as the former Dortmund striker came back to haunt the club he left for the capital in July.
And Dortmund coach Jurgen Klopp will be without Mkhitaryan for their final two games before the mid-season break - against Wolfsburg and Werder Bremen - as the Ruhr club look to arrest a dismal season which sees them currently sat in the Bundesliga's relegation play-off place.
A club statement revealed Mkhitaryan suffered a tear in his right hamstring, with a recovery period of six weeks.
Dortmund host Wolfsburg on Wednesday before rounding off their first half of the campaign at Bremen's Weserstadion.
Mkhitaryan will hope to return to action when Dortmund resume their season away to Bayer Leverkusen at the end of January.
