The teenager limped off in the first half of the goalless Edinburgh derby after putting in a strong sliding tackle on Hibernian winger Matt Done.
Interim manager Gary Locke told Hearts TV: "He's got a bad one. We'll see how he responds to treatment.
"I'm hopeful that he'll be okay but he is in the hands of the physios at the moment.
"If they can work their magic then hopefully he will be in contention but it's still too early to say at the moment."
Hearts already have defenders Danny Grainger (knee), Jamie Hamill (knee) and Marius Zaliukas (ankle) on the injury list but Darren Barr will return from suspension to join the squad to face St Mirren on Sunday.
Brad McKay, another 19-year-old, replaced Mullen to make his Hearts debut at Easter Road on Sunday.