Mkhitaryan fractured his metatarsal playing for Arsenal in their EFL Cup defeat to Tottenham last week.
He was subbed off at half time and subsequently missed the 3-1 win over Burnley at the weekend.
Mkhitaryan has been ruled out for six weeks, meaning he likely won’t be back in acton until the end of January.
But the ex-Manchester United playmaker posted a positive message on Twitter for fans on Christmas Day.
Smiling at the camera, he wrote: “Really touched by all your wishes for a prompt recovery.
“Thank you Fans! Coming back stronger.”
The message was well received by Arsenal fans, who are keen for the Gunners to kick on after an excellent start to the season.
Arsenal only saw a 22-game unbeaten run ended this month when they were downed 3-2 at Southampton.
They recovered from the Saints and Spurs defeats to beat Burnley at the weekend and face Brighton on Boxing Day.
Mkhitaryan will likely miss games against Liverpool, Fulham, West Ham and Chelsea.
He will also be out of the FA Cup third-round tie with Blackpool on January 5.
All being well, Arsenal could have him back for a clash with Cardiff on January 29.
However, a more realistic return date may be the Manchester City clash at the start of February – or even Arsenal’s trip to Huddersfield on February 9.