The 20-year-old made 14 appearances for Port Vale last season and made his debut in Shrewsbury's 1-0 victory over York City on Saturday.
"I'm willing to fight for my place and hopefully, given a chance, I will be able to do that," Grimmer told the club's website.
"I am not expecting to come here and be a nailed-on certainty to start because that's not how football works.
"I spoke to [Micky] and he is under the impression that I will fit in nicely to the way he wants to play."
Grimmer joins Shrewsbury alongside fellow loanee signing Bobby Grant, who has arrived from Blackpool.