Oates will have the operation on Saturday after being collected high by North Queensland fullback Scott Drinkwater immediately after halftime in the Broncos' 28-16 win at Suncorp Stadium the previous night.
Drinkwater was put on report over the incident.
Brisbane's outside back Jesse Arthars is expected to come into the starting lineup for the NRL round three clash at the same venue with St George Illawarra next Saturday.
Oates has been a key plank in the Broncos' renaissance under coach Kevin Walters.
He scored a career-best 20 tries last season and returned to Queensland's State of Origin side after a three-year absence to play a crucial role in the series decider.
Walters said Oates was "a big loss".
"He is just tough. He is an old pro Oatesy, from way back," he said.
"He is very reliable with his carries out of yardage, he's a good finisher and good under the high ball."
Arthars was outstanding against Penrith in the 13-12 win in round one and had a hand in a key try after halftime in the win over the Cowboys.
"He is a different body shape to what Oatesy brings but he certainly brings a different skillset. At times this year he has been really good," Walters said.
"He played last week against Penrith and caught every bomb and today he was instrumental with one of the tries with his speed and acceleration."
Walters said Drinkwater's tackle, as Oates was steaming towards the tryline, "wasn't a very good incident to have in our game".
When asked if he thought a sin-bin was sufficient, Walters said "probably not".
Broncos captain Adam Reynolds said he questioned the referee on the decision just to sin-bin Drinkwater but conceded with everything happening at such a high speed it was difficult for officials.
"When you look at the replay it doesn't look too good," he said.
"We lose a player for the game and for a number of weeks probably. Whether ten minutes is justifiable, I don't think so."
Walters said he trusted the NRL to make the right call.
"We will get around Oatesy and support him with his recovery and back to playing," he said.
Cowboys coach Todd Payten said he was comfortable with the sin-binning of Drinkwater "so long as it is consistent all season long".
"Scott's tackle happened really quick. Corey changed direction really late. He was trying to stop the try," Payten said.
"He has one foot on the deck and no intent to make collision with where he got him. It was certainly an accident. The kid was just doing his best to stop a try really quickly."
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