Mkhitaryan picked up the knock in an off-the-ball collison with Marek Suchy during his country's friendly with the Czech Republic on Wednesday and was taken off in the 38th minute as a result.
Test results on the 27-year-old's thigh injury were "not encouraging" and he now faces a race against time to be fit for one of our biggest games of the season against Pep Guardiola's Manchester City side on September 10.
He is set to return to Carrington where he will be further assessed by United's medical staff ahead of next Saturday's encounter at Old Trafford.
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 and 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 ten days to heal which means that Mkhitaryan will miss the Denmark-Armenia match on September 4."
The attacking midfielder, who signed from Dortmund in the summer for £22 million, has only made three substitute appearances for the Reds but was thought to be in contention for a starting place in the derby after impressing off the bench at Hull.
His likely absence, however, means that Juan Mata will probably retain his right-wing spot
as Jose assesses his options ahead of next Saturday's showdown.
The boss will be forced into at least one alteration to his line-up as Marouane Fellaini is out with a back injury and Antonio Valencia could also miss the match as he does not return from Ecuador duty until Friday night.
Regarding the international break, Mourinho said:
"We keep eight outfield players and the goalkeeper (Sam Johnstone) for training, we are going to lose the others and we don't know the way they train, the way they recover, the life they are going to have with their countries.
"It is always a difficult situation but we know it is like this when we have these players- and I would love all of the players to go because it would mean that everyone is being selected for their national teams and that is always a great privilege."