The injury was sustained in November's defeat by Inverness Caledonian Thistle before more recent scans identified the full extent of the damage.
But Clark had tried to continue running after doing the damage having thought he had only cut his ankle.
He told the Daily Record: "I knew it was a sore one when it happened but I didn't know how bad.
"I got up and ran across for the ball at the touchline and at that point I realised there was something seriously wrong.
"I didn't think it was a break, though. I thought it was just a bad gash.
"In fact only last week I started running again but it still wasn't right and it was only after I went for another scan they realised I had chipped some of the bone around the ankle.
"It's pretty bad and they can't tell me how long I can expect to be out. It's frustrating, because I was in the side and we were doing well.
"We could have gone top of the league that night and it's frustrating to be on the sidelines watching when you can't help the lads.
"There's not much I can do. I just need to work hard to try to get back as soon as possible."