Ansbro sustained the injury during a pre-season tour match with London Irish 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."
While London Irish have yet to set a date for the centre's return, Scotland team doctor James Robson expects him to resume playing in around three months.
Robson's prognosis means the 26-year-old will miss the autumn internationals against New Zealand, South Africa and Tonga.
"The management of the injury Joe has sustained typically involves a period of between six and eight weeks' immobilisation," Robson said.
"After that there will be a further four to six weeks of rehabilitation before he can look at a return to the game. We wish Joe well in his recovery."
Ansbro has won 11 caps after making his debut against South Africa in 2010, scoring three tries, including one against Romania in last year's World Cup.
Born in Glasgow, he joined London Irish last summer after beginning his club career at Northampton.
Ansbro's father Paul revealed there was nothing malicious behind the injury and was relieved his son escaped more serious damage.
"He's got a triple fracture of the C1 vertebrae at the top of his spine," he told BBC Scotland.
"They've put a metal halo on his head that's got to be in place 24/7 for three months.
"They did a CAT scan and an MRI scan and they've had a neurosurgeon looking after him.
"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.
"Your blood runs cold when you hear about it and it's something that every parent worries about.
"It's a fantastic, rough game and these things, unfortunately, cannot be ruled out."