The Rugby Football League announced that Burgess had been referred to a disciplinary hearing.
"The Match Review Panel appointed by the Rugby Football League for the series determined that the incident merits a Grade D charge of behaviour contrary to the true spirit of the game," it said in a statement.
A grade D offence carries a suspension of three to five matches, which puts Burgess' place in the team for Sunday's third test against the Kiwis at Elland Road in doubt.
Any further bans will be carried over into the 2019 NRL season.
Watene-Zelezniak confirmed the fingers of Burgess plunged into his eye but brushed it off in his post-match interviews.
"I felt a finger go in my eye," Watene-Zelezniak said. "That's football. Lucky the doctor was there to give me something. It was a bit blurry after that. Whatever he gave me it helped a lot.
"That's international football. I'm a tough boy, I'm an adult, I'm a man so I can take those kinds of things but what I can't take is a loss."
Watene-Zelezniak was unsure if Burgess' act was intentional.
"I have no idea I'd have to watch the video back. He's a big boy and he's got some big fingers too. I think his whole hand would probably cover my whole face.
"I'm sure he didn't do it on purpose him and his brothers are good guys and they've done really good things for the game. I don't think that's in their kit bag but it is what it is you just have to deal with it.
"I'm pretty sweet now. The doctor gave me some kind of eye drops. I'm sure it was accidental. It didn't really mess with the game much but that's football."
