Ansbro sustained the injury during a pre-season tour match and remains at University Hospital, Cork. He will return to the UK later this week.
"Joe broke a small bone at the top of his neck early in the game's second half," read a statement released by London Irish.
"After An MRI scan, it was confirmed that immediate surgery was not required, and the injury would be managed by external fixation.
"He is in the care of the club's and hospitals medical team and is expected to return to the UK later this week."
Ansbro's father Paul told BBC Scotland: "He's got a triple fracture of the C1 vertebrae at the top of his spine. They've put a metal halo on his head that's got to be in place 24/7 for three months.
"He was really lucky that it was what they call a stable fracture and there's no nerve damage. That was the thing they were most concerned about; Joe's still got movement in his hands and feet."
The player's father also said there was "nothing malicious" in the tackle that led to the incident.
Ansbro has 11 Scotland caps and has been with London Irish since 2007.