Grimes landed on his shoulder after a heavy first-quarter tackle in Melbourne's 61-point loss to Carlton on Sunday, and immediately left the field cradling his left arm.
The 23-year-old was subbed out of the contest and had the injury assessed, with the Demons likely to be without the midfielder until the back end of the season.
Injuries have limited Grimes to only 59 games with the club, having been struck down by back, hip and groin problems. He also suffered a season-ending navicular injury to his foot in 2011.
Grimes' early injury forced the Demons to change some of their plans, but coach Mark Neeld credited Grimes' for his attack on the ball.
"He's had a couple of injuries, Jack. That's part of the game," Neeld said post-match.
"He's a courageous young fella, Jack, and you put your head over it, and put your nose over it, these things happen."
The Demons had 110 fewer disposals than Carlton in the defeat, and 14 fewer tackles.
The margin in statistics was not quite reflected on the scoreboard, with the Demons' effort clearly lifted from early-season defeats.
Neeld said the gap in experience between the sides had a major effect on the result, admitting his team needed a few years' worth of games before matching it consistently with the best sides.
"There's probably four or five sides in the competition going through the same thing that have similar experience levels…that composure with the ball, the ability to deal with the opposition's pressure, that's the stuff that needs to become ingrained," Neeld said.
Five talking points: Carlton v Melbourne
"Watching the Kangaroos play the other day I heard Scotty (Brad Scott) talking about they're now getting to the 80-plus average game mark, and they're able to go for longer. He's got his boys with some ingrained things that are really good.
"We're probably two years behind that so we've got to make sure that's ingrained [by] then."
The Demons will have an addition of experience next week, with off-season recruit Chris Dawes looking set to make his Melbourne debut next Sunday when the Demons host Gold Coast at the MCG.
Dawes kicked three goals in the VFL on Saturday for Casey Scorpions in his return from a hamstring injury.
Follow AFL website reporter Callum Twomey on Twitter at @AFL_CalTwomey
