Holohan also missed the previous match against Bristol Rovers with a groin issue and has since been for a scan to reveal the extent of his injury.
Shelton suffered a bruised calf on Saturday and travelled down to Sutton but manager Dave Challinor opted not to risk the midfielder.
The Pools boss admitted Holohan’s injury is more severe than first feared but there is no clear time frame as to how long the Irish midfielder will be sidelined.
"Gav has had a scan and results wise it's more severe than what we thought,” he said.
“Scans don't always tell the true story at times because Gav feels quite good in himself but is going to be a little bit longer than anticipated.
"I'm saying that based on the scan because if you'd asked him prior to having it how far away he was, he'd have said back training Thursday and available for the weekend.
"We just need to see how he progresses day by day and if he's available in two days time then brilliant, two weeks a little bit more disappointing, four weeks even more, it's one we have to play by ear.”
On a more positive note, Shelton is expected to return to training on Thursday and be back available for Saturday’s League Two trip to Oldham Athletic as Pools look to pick up their first away points of the new season.
“Shelts should be fine for the weekend, he took a whack on his calf on Saturday and it's bruised and swollen,” Challinor added.
"We could have played him [at Sutton] but if he got a kick on it then he would have had to come off.
"So we didn't want to potentially be forced into a change early or having to make another change if he came off the bench and took a whack.
"With Gav being out as well, we took a safe bet to leave him out which will hopefully mean he's fine for the weekend.”