Burgess has also been fine £500 ($900).
The Rabbitoh was playing for England during their Test win against New Zealand on Sunday when, about 60 minutes in, he appeared to gouge Dallin Watene-Zelezniak's right eye.
Burgess' suspension comes despite the incident going unpunished by referee Gerard Sutton at the time during the second-half of the match at Anfield.
Burgess was found guilty of behaviour contrary to the true spirit of the game (gouging) by an global disciplinary panel following an incident in last Sunday's second Test against New Zealand at Anfield, and the suspension will rule him out of this Sunday's third Test at Elland Road.More news: Filipino graphic novel series to become Netflix anime
The suspension will rule him out of this Sunday's third and final Test at Elland Road, as well as the 2019 NRL season.
"It is not in my makeup as a rugby league player and never has been".
Burgess pleaded not guilty at an worldwide disciplinary panel on Tuesday after being charged by the Rugby Football League.
England's win in Liverpool means they have already secured the three-match series with one game to play.More news: European football leagues oppose potential Super League
"Lucky the doctor was there to give me something".
However, the Penrith star brushed it off and said he was sure that Burgess' act wasn't intentional. He's a big boy and he's got some big fingers too. I don't think that's in their kit bag but it is what it is you just have to deal with it. He is a big boy with some big fingers, so his hand on my face probably covers it all.
"I'm pretty sweet now. It didn't really mess with the game much but that's football".
Burgess was recalled by England from a two-year absence for the opening autumn worldwide against France and he also played in both games against the Kiwis so far.More news: South Korean minister: United States says N. Korea canceled meeting