Grandison, one of six players to have been offered a new contract by the club, faces a lay-off until Christmas after advice from a specialist.
"It looks likely that he'll require surgery on his hip which is quite an extensive operation," manager Graham Turner told the club's official website.
"He could be out for quite some time. The fear is it could be up to six months which will be a severe blow to us because he's very much an integral part of what we had planned.
"He can play as a central defender, which we've seen, and the enjoyment of playing right-back where he gets forward and I think the crowd have taken to him as a right-back with his little stepovers, his tricks, and his power up and down the right-hand side.
"If he's going to be out for that length of time, it will be a severe blow to us, but we'll get over it."
Tom Bradshaw, Connor Goldson, Jon Taylor, Aaron Wildig and Ryan Woods have all been offered new deals by the Shrews.
"They have a month from the time they receive their offers so it's just over a week has gone by since that," Turner added. "We just have to wait and see what happens now."