The 20-year-old Coventry centre-back, who has already enjoyed two successful spells with Tranmere this season, has signed an initial one-month loan at the Greenhous Stadium and could be thrown straight into the starting line-up.
However, having had no time to train with his new club, Grandison may have to settle for a place on the bench.
Full-back David Raven will be missing for the Shrews after irritating a hip injury in training this week.
The 25-year-old played through the injury in the 3-1 defeat to Morecambe but pulled up during training in midweek and could now face up to three months on the sidelines if surgery is required.
Craig Disley, who has also been suffering from a hip problem, has returned to fun training but is not expected to feature.