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.
Arsenal star Henrikh Mkhitaryan was injured in the defeat to Tottenham (Image: GETTY)
Arsenal will hope to have Henrikh Mkhitaryan back for February (Image: GETTY)
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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.