The Fiji-born 31-year-old had a medical episode on Monday and was rushed to hospital, with the club confirming the shock diagnosis.
"He has undergone treatment for a suspected stroke and is recovering in hospital," the club said in a statement.
"Tui is receiving the best possible care and is being supported by hospital specialists, alongside the club's medical staff."
Kamikamica's immediate playing future is unclear.
The Storm had already lost fellow forward Eliesa Katoa for the season after he required brain surgery due to bleeding on the brain following a series of head knocks while playing for Tonga last November.
Coach Craig Bellamy said in a recent interview he wasn't sure if 26-year-old Katoa, who is still with the club, would be able to play in the NRL again.
Fiji captain Kamikamica played for Melbourne in Saturday night's tight NRL loss to North Queensland, coming off the bench for 25 minutes of game time.
The team travelled back from Townsville on Sunday after giving up a 10-point lead to suffer back-to-back defeats for the first time since the start of the 2025 season.
Kamikamica, who has a young son also called Tui, was linked to the UK Super League before signing a deal to remain with Melbourne for the 2026 season.
With Nelson Asofa-Solomona leaving the club to pursue a boxing career, he has become a linchpin in the Storm's forward pack.
Making his NRL debut with Melbourne in 2017 and playing 142 matches including their last two grand final losses, Kamikamika has regularly spoken of his strong ties to his homeland.
The Storm are planning to travel to Sydney on Thursday afternoon ahead of their Good Friday clash with unbeaten Penrith at CommBank Stadium.
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