After scoring United's fourth goal of the tie in the 16th minute of the second leg at Stade Geoffroy-Guichard, Mkhitaryan was replaced by Marcus Rashford just nine minutes later due to an apparent hamstring injury.
The Armenian forward tweeted after the game to say how happy he was to have scored on his return to France, where he grew up when his father was a striker for the now defunct ASOA Valence.
The 28-year-old acknowledged his concerns over missing out on United's day out at Wembley, when they face Southampton in the EFL Cup final, by including the words "fingers crossed" in his tweet.
United manager Jose Mourinho also has a doubt over the fitness of Michael Carrick for Sunday's final, the midfielder went off shortly after the hour due to a calf complaint.
The Portuguese said he thinks both players will miss the game against the Saints.