The Armenian FA confirmed the midfielder has suffered a thigh injury which could take around 10 days to heal.
Mkhitaryan picked up the knock in an off-the-ball collision with Marek Suchy during the first half of Armenia's friendly with the Czech Republic on Wednesday and was taken off as a result.
The Armenian FA ruled Mkhitaryan out of their game against Denmark on Sunday and he will now return to Carrington to be assessed by United's medical staff.
A statement released by the Armenian FA read: "As reported, senior national team captain Henrikh Mkhitaryan received an injury against Czech Republic and as a result was unable to continue the match.
"Mkhitaryan has had a medical examination in a clinic in Mlada Boleslav. Unfortunately, the results are not encouraging.
"Mkhitaryan was found to have an injury in the lower third of the left thigh muscle. Such injuries usually require a week to 10 days to heal, which means that Mkhitaryan will miss the Denmark-Armenia match on September 4."