The centre-back, whose turnaround in form was instrumental to AFC's eight-game run of shut-outs, suffered an injury to his knee in Saturday's thrilling 3-3 draw.
The 25-year-old signed a new contract with the club last week but had a nightmare second half against the Dees, gifting Gary Harkins Dundee's third goal of the game then picking up the knock.
Big Ashton is now due to undergo an operation on Wednesday and could miss first-team action until March wile he recovers, missing the League Cup semi-final and possibly the late February showdown with Celtic.
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