Cleary beat out Braydon Trindall to take home the NRL's top gong on Wednesday night, giving him a complete set of major rugby league awards.
The 28-year-old was unable to attend the awards night, after being released from hospital on Wednesday following emergency surgery on his ankle.
AAP understands the surgeon is so far happy with the outcome of the operation, with a hope Cleary will be able to return to the field for round one.
The Penrith halfback will also soon undergo surgery on the broken right foot he carried into Sunday's preliminary final against Newcastle, but that should recover quickly.
The development is a positive for Cleary, who has been overwhelmed by the support since he suffered a compound fracture and ankle dislocation in Sunday's loss.
The NRL first raised the prospect of needing to take the award to Nathan on Tuesday, before it was presented to the halfback on Wednesday.
"I want to start off by saying how grateful I am for everyone's support over the last few days given the injury that happened," Cleary said in a pre-recorded speech.
"The support from the rugby league community has been absolutely amazing. I can't thank everyone enough for the messages they've sent through.
"In terms of being able to win the Dally M award, I'm super grateful for that as well."
The No.7's injury remained the talk of the Dally Ms on Wednesday night, with Penrith players still coming to terms with the blow.
Penrith's sheds after the injury at halftime have been described as particularly quiet, as players came to terms with the situation.
"To see him playing through his injury already, and then what happened. Super gutted for him," centre Casey McLean said.
"I can't put more words together for his dad, Ivan, to sit through another half of footy when watching your son with what happened.
"You don't want to see that happen to anyone, let alone your own teammate and captain. But we still had opportunities to win and it just got away from us."
Footage has also emerged of fullback Dylan Edwards trying to stop Cleary from looking at the injury, with his foot pointing the wrong way.
"I was just trying to keep him calm as I could," Edwards said.
"To his credit he is a tough person. And the way he was handling that was incredible.
"It was gut-wrenching, something you're not used to seeing on the footy field. It was pretty hard to see, especially to one of your great mates."
Edwards, meanwhile, is still hopeful of being able to represent Australia at the World Cup after avoiding knee surgery following a PCL injury in the loss.
"I'm not sure, I have to talk to Kevvie (coach Kevin Walters)," Edwards said, while wearing a brace at the Dally Ms.
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