Katoa was on Monday recovering in an Auckland hospital following surgery, after requiring an oxygen mask on the sideline during Tonga's 40-14 defeat to New Zealand on Sunday.
The Storm second-rower was first collected by teammate Lehi Hopoate in a pre-match warm-up, but was deemed to not require a head injury assessment (HIA) after being looked at on-field by Tonga medical staff.
After taking the field he suffered further friendly fire when his head collided with Will Penisini in the 10th minute, before being taken off and passing a HIA.
But he suffered a third knock to the head trying to tackle New Zealand forward Naufahu Whyte in the second half, again resulting in him leaving for a HIA.
Katoa was then immediately ruled out of the game, as NRL rules dictate that if a player leaves the field for two HIAs they cannot return.
AAP understands the 25-year-old suffered bleeding on the brain, but it's believed he isn't expected to suffer any long-lasting effects.
"Eli Katoa was taken to hospital after suffering seizure activity on the bench during the second half of yesterday's Pacific Championships match between Tonga and New Zealand," Melbourne said in a statement.
"Eli underwent surgery overnight and is in a stable condition being supported by his partner and mother.
"Storm medical staff remain in close contact with the hospital and Tonga's team chief medical officer."
Katoa is said to be in good spirits, and has messaged Storm teammates to thank them for reaching out to him.
He also took to Instagram on Monday morning to post a photo of several needles in his arm, along with verse from the Bible.
"Appreciate everyone for checking in," Katoa said in the Instagram story.
"Sorry if I haven't got back to any of you guys but I really appreciate all the love and the messages Ofa atu (I love you)."
Tonga coach Kristian Woolf said after Sunday's game that the doctors had been confident Katoa was fine following the pre-match collision with Hopoate.
It is understood that replays were not immediately available to Tonga's staff when Hopoate's shoulder collected Katoa's head.
"We have two very experienced doctors there, they have done the usual (tests). He has passed all that and passed it well," Woolf said.
"My job is not to question doctors.
"They were both comfortable with that and comfortable with him coming back on to the field."
The NRL will make inquiries into the matter, as will the Rugby League Players' Association.
"Ensuring a safe environment for players is the remit of the NRL," RLPA chief operating officer Luke Ellis said.
"So along with our own enquiries, we will be trusting them to work through this and understand what occurred."
Samoa stars Jarome Luai and Junior Paulo said they were "heartbroken" to see Katoa's situation, with Paulo stressing the importance of players' health being put first.
"We as footy players will probably never say no to turning up for your country and getting out there and playing," Paulo said.
"There are protocols around that and should be followed - and they probably were followed.
"In terms of putting your health before your job, that's probably the main outcome that we really want to take out of it."
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