The 28-year-old was injured late in United's 4-1 Championship victory at Firhill and, as feared, now faces a lengthy spell on the sidelines after undergoing surgery on Sunday.
However, the club intend to show their support for the stricken player by confirming a new contract in the coming days.
United's sporting director Tony Asghar said on the club's website: "Everyone at United is gutted for Nicky. He has had a tremendous season so far, and his contribution of goals and consistent performances have played a massive part in us being in the position we find ourselves in currently.
"On the upside, we have agreed terms with Nicky to extend his current contract to keep him at the club until at least the summer of 2021 and should confirm that in the coming days.
"Nicky will have an operation today and then start his rehabilitation in the good hands of our medical team at the HPC at the University of St Andrews."
Clark himself wrote on Twitter: "Great win yesterday, unfortunately the injury isn't good but it happens in football. No doubt the boys will keep the run going and I'll be there to support them!! Thanks for all the messages much appreciated."
Saturday's win saw United extend their lead at the top of the Championship to 17 points, with second placed Inverness having a game in hand as they were one of several sides to see their match postponed due to the weather.