The Celtic loanee posted a picture of himself on Instagram in a hospital bed with the caption “operation complete”.
Allan was substitute before half-time in a 4-1 defeat to Rangers last month. It was suspected the move was tactical, though manager Neil McCann later insisted the player was struggling with a recurring issue.
Though he returned to the starting XI for the 1-1 draw with Kilmarnock on 23 September, Allan has been an unused substitute in Dundee’s two other league fixtures since the Ibrox defeat.
A Dundee spokesman has confirmed that the operation was a means of solving the groin problem, but couldn’t yet give an accurate estimate for how long the player will be out for.