The young hooker looked troubled as he left the captain's run on Wednesday and was later ruled out with an adductor injury.
He's only expected to miss one week and should be available for the Queensland team for the opening State of Origin in Sydney on June 8.
Storm coach Craig Bellamy is hopeful Grant will be available for the AAMI Park match, where his side attempt to arrest a rare two-game losing streak.
"I'm not exactly sure what he's done but he felt a bit of tightness," Bellamy said of Grant after training.
Brandon Smith has now been slotted in at hooker while interchange forward Alec MacDonald will also miss the round-12 match due to illness.
Jordan Grant and Chris Lewis come onto the interchange bench.
The coach was relieved to see halfback Jahrome Hughes get through the session after missing their two losses with a calf injury.
They also have first-choice fullback Ryan Papenhuyzen sidelined with knee damage.
"(Hughes) hasn't done all that we've done this week but he got through most of it and seems to have come through OK so he should be right," Bellamy said.
Melbourne had club great Greg Inglis address the players before he watched on at training ahead of Indigenous round.
Former Test and Origin star Inglis is set to lead the Storm out onto the ground on Thursday night and Bellamy joked he looked fit enough for a 20-minute run.
"He's a really important part of our history," Bellamy said.
"Everyone knows how talented and competitive he was and just how good he was, but he was also a great club man."
Melbourne were hammered by North Queensland 36-6 last Saturday night, having suffered a 26-point loss to defending premiers Penrith the previous week, but still sit second on the ladder behind the Panthers.
Bellamy said the team "lacked effort" against the Cowboys and he demanded a response this week.
Manly are coming off a narrow loss to Parramatta and have dropped outside the eight to 10th, also losing superstar fullback Tom Trbojevic for the season with a shoulder injury.
"They've had an up-and-down season but they were very unlucky not to get a win last week," Bellamy said.
"There's some real competitors in that team and obviously losing Tom - he's such a great player and has had such a tough run - but I think (Reuben) Garrick can do the job."
Meanwhile, Bellamy dismissed criticism of the Storm's tackling technique after Cowboys stars Jason Taumalolo and Kyle Feldt both suffered knee injuries during their clash.
They were hit by tacklers coming in low and high from different angles although they were cleared by NRL head of football Graham Annesley as "just legs tackles".
"Do we need to get out the protractors and work the angles out that we come in?" Bellamy bristled.
"We didn't have anyone charged at the weekend or last three weeks or four weeks or five weeks."
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