The right-back went down innocuously at the halfway line with ten minutes remaining and the home side 3-0 up.
They were forced to finish the match with ten men after using up all of their substitutes, though Aidan Keena added to goals from Christophe Berra, Demetri Mitchell and Steven MacLean to see them safely through to the quarter finals.
Manager Craig Levein revealed the nature of the injury after the match, though he couldn't put an exact timeframe on the Northern Ireland international's recovery until the full extent of the damage has been revealed.
He said: "The one big downside is that Mick - who was as professional as ever in his performance today - has torn his thigh muscle, unfortunately.
"He's getting a scan tomorrow so it depends on how bad it is, whether it's a grade one, two or three.
"It was his standing leg when he passed the ball. It might be six weeks if it's a grade two or it might be longer.
"Obviously we're not allowed to have all our players fit."