Town manager Paul Simpson confirmed to BBC Radio Shropshire: "He's got a grade two tear of the groin, which could put him out for three or four weeks."
It leaves Town low on numbers following defender Shane Cansdell-Sherriff's red card against Rochdale on Saturday.
And Simpson is aware that he may need to bring in a loan striker to cover for Hibbert.
"I don't know if we can," he said. "I'll have to speak to the chairman and find out his thoughts on it."
Simpson was more preoccupied with losing Cansdell-Sherriff for another game when he brought down Rochdale's Chris Dagnall, who was through on goal 15 minutes from time on Saturday.
It was stupid. Childish. You wouldn't see that on a parks pitch
Town boss Paul Simpson on Shane Cansdell-Sherriff's red card
"It was stupid," said Simpson. "Childish. You wouldn't see that on a parks pitch.
"When you get ridiculous decisions by players to bring lads down and get sent off then it costs you even more."
The Aussie right-back, who was only making his return to the Town team after a two-game ban for picking up 10 bookings, was given a straight red card.
Shrewsbury have now picked up just four points out of a possible 15, having won just once in five games, in which they have scored just twice.
Apart from Hibbert's sudden goal drought (he has not found the net since equalling an individual club scoring record on 23 January), Jake Robinson has scored just three times this season and Kris Bright is yet to score in 19 appearances from the bench.
And, more crucially, Norwich City loan man Jamie Cureton is still looking to get off the mark since his debut five games ago.
Source: BBC Sport
Source: BBC Sport