The Melbourne prop suffered the suspected stroke at home on Monday.
Kamikamica, who has played 142 NRL games, will begin the next stage of his recovery at an inpatient clinic, with the Storm aiming for the 31-year-old to then integrate back into their own rehabilitation program alongside injured players.
The Storm did not put a timeline on Kamikamica's return to the field in a statement released on Thursday morning, but a comeback in the short term appears unlikely.
Teammates visited Kamikamica in hospital earlier in the week, and coach Craig Bellamy has been buoyed by the prop's attitude to his recovery.
"I exchanged texts with him there yesterday and he's always ultra positive," Bellamy said.
"He says he'll be back soon, but it's more of a thing for our medical people to explain what's going on.
"He's always up and about and we all love how fit and strong he is, and for him at that age, to suffer from that, was a shock to everybody."
From a football perspective, Kamikamica's absence leaves the Storm without another big body in the middle of the park, already an area of focus for recruitment since Nelson Asofa-Solomona's off-season exit.
The club have replaced Kamikamica with 2024 grand final player Lazarus Vaalepu for the Good Friday clash against red-hot Penrith.
But Bellamy was unsure whether the club would be given special dispensation to go to market and replace Kamikamica in their top-30 squad.
"That's a good question and I might ask it. At the moment we're just concerned with Tui making a full recovery," he said.
Melbourne are already without Eli Katoa, who suffered a brain bleed in the wash-up from a Test match between Tonga and New Zealand late last year.
Katoa has been sidelined from the 2026 season, and Bellamy admitted last month he was unsure whether the star second-rower would play again.
In their press statement, the Storm thanked hospital staff for their care of Kamikamica.
"The club would like to thank the medical professionals at Royal Melbourne Hospital and Ambulance Victoria for their outstanding care of Tui and extend its appreciation to everyone who has supported Tui and his family during this difficult time," a spokesperson wrote.
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