Law firm Maurice Blackburn said the asylum-seeker, who is aged in his 30s but was not named, had his right eye removed and a titanium plate and screws inserted into his face.
It followed "severe head trauma", a ruptured eye and fractures he suffered during unrest in February at the camp on Manus Island.
"Our client has suffered enormously, both physically and psychologically, because of what we say is the failure of the (Australian) Commonwealth and G4S to provide a safe and secure environment for people at the Manus Island detention centre," Maurice Blackburn principal Jane McDermott said.
She added that the man - who arrived in Australia by boat from Indonesia in October - was suffering post-traumatic stress disorder (PTSD), depression, anxiety and suicidal thoughts, and was also being assessed for a brain injury.
The case was filed in the Victorian Supreme Court, which allowed the man to use the pseudonym RN as he feared identification could place him and his family in danger.
The violence at the camp - which an investigation found was fuelled by frustration and uncertainty about the detainees' fate under Canberra's hardline immigration policy - left one Iranian asylum-seeker dead and 69 people injured.
Boatpeople arriving in Australia since July 2013 have been sent to camps on Manus Island and Nauru. They will be resettled in those countries if their refugee claims are valid.
Maurice Blackburn said the asylum-seeker's eye was replaced with a prosthetic implant following treatment at a Brisbane hospital.
He is currently being held at the Villawood Immigration Detention Centre in Sydney.
The man said he feared being sent back to Manus Island and that he had "not felt very good, either physically or mentally, since I was brought to Villawood".
"I was inside (the Manus Island camp) when the attack started. I went outside to see what was happening," he said in a statement.
"When I went outside, I was hit in the right eye with a rock. I knew straight away that my eye had been badly damaged."
The first court hearing will be on September 13.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ