Pilkington picked up a hamstring problem during his side's 2-1 defeat to Newcastle United last weekend, while Snodgrass suffered a knee injury in training.
"Anthony has had a scan which shows a grade two strain which usually means five or six weeks out," ITV Sport quotes Hughton as saying.
"Robert came back from international duty with Scotland and felt his knee at the beginning of training on Friday.
"He travelled with us to Newcastle as we hoped it would settle down, but unfortunately it didn't, and he could be out for a few weeks but not as long as Anthony."
Hughton was speaking at the club's annual general meeting.