Katoa was hospitalised in Auckland on Sunday night, after requiring an oxygen mask on the sideline during Tonga's 40-14 defeat at Eden Park.
The second-rower was first collected by teammate Lehi Hopoate in a pre-match warm up, but it was deemed he did not require a head injury assessment.
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 then 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.
Melbourne officials have confirmed to AAP that the 25-year-old subsequently suffered bleeding on the brain, but they are hopeful of no 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," the club 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.
"We have two very experienced doctors there, they have done the usual HIA. 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.
"Unfortunately he copped a second hit that was quite heavy, and there has been a bit of a poor result on the back of that."
9°C