Clarke missed last weekend's derby with Leeds United due to an ongoing hip issue, which had earlier seen him volunteer to play through the pain barrier to score a goal from the bench in the 3-2 win at Brentford.
Wilder said: "We had to wait for the results of the scan and it is disappointing for ourselves and Leon. He had a bit of a setback after the Brentford game where he played through the pain barrier.
"Unfortunately, it has knocked him back a little bit.
"He was really disappointed not to be invovled last Satuday and that is always a good thing - when you have got players who want to play. Hopefully, if it is not right for the weekend, he will be okay for Friday night.
"We are not expecting it to be a long-term injury.
Meanwhile, Wilder has confirmed that Liverpool loanee Ben Woodburn will miss the weekend trip to Reading due to an ankle ligament injury.
Wilder added: "Unfortunately, for Ben, he got injured in training. That is disappointing for him as well and we are assessing that at the moment.
"He has gone off for a scan this week and is definitely ruled out for the weekend. We are assessing how long that will be, but hopefully it will not be too long."