Cleary was rushed to hospital in Penrith's season-ending 22-14 loss to Newcastle on Sunday, after suffering a compound fracture and ankle dislocation.
Knights hooker Phoenix Crossland was on Monday referred straight to the judiciary over the incident, with the hip-drop tackle set to rule him out of the grand final.
Cleary posted on Instagram on Monday, confirming he had successfully undergone surgery on his left foot.
"Thank you so much to everyone that has reached out, the support has been unbelievable," Cleary wrote.
"Yesterday sucked but it's all part of the journey & it's made me even more grateful for the people I have around me. I'll be back."
Another surgery is still required on Cleary's right foot, after Penrith revealed the No.7 had broken a bone in it during the week-one finals win over Sydney Roosters.
Those injuries will render Cleary unable to attend Wednesday night's Dally M ceremony at Barangaroo, where the playmaker is expected to win the top medal.
The Dally M is the one prize that has so far eluded Cleary throughout his illustrious career, but he is the strong frontrunner to claim this year's prize.
The two-time Clive Churchill Medalist held a healthy lead at the top of the leaderboard when votes went behind closed doors after round 12.
So gory was Cleary's injury, one Penrith official compared it to a gunshot wound when he returned to the sideline after the halfback was stretchered off on Sunday.
"It was really difficult to watch," Sydney Roosters veteran Daly Cherry-Evans said on Monday.
"I'm sending out all my love to him and his recovery process. I hope it goes really smoothly.
"I watch it through the lens sometimes as a dad, and watching his dad up in the coach's box, I just could not believe how he would be able to sit there, compose himself, and coach a side when his son has just had a pretty rough injury."
What Cleary's injury did prove is the kind of damage that must be done to remove one of Penrith's players from the field in a big match.
Dylan Edwards is also injured and suffered a suspected PCL rupture in the first half of Sunday's loss, but soldiered through.
He is now in doubt for the World Cup, with fellow fullback Reece Walsh also in a race against the clock for Australia's October 15 tournament opener against New Zealand.
Blaize Talagi ruptured his Achilles tendon in the second half, while Australia captain Isaah Yeo has admitted he may too have to pull out of the World Cup.
The Penrith lock had put off surgery on a ruptured pectoral muscle to play in the Panthers' finals series, but still needs to go under the knife.
"I don't know if I'll be available yet, I'll have to talk to the club as well because it will affect the start of next season if I was to prolong it," Yeo said.
"That's a conversation for probably later on next week with Ivan and the staff."
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