The 21-year-old was injured during Saturday's 55-19 win over the USA Eagles in New Jersey.
Ulster's Paddy Jackson has joined up with the Irish squad for the matches against Japan on 17 and 24 June.
Carbery had a mixed game against the US, twice having clearance kicks charged down leading to tries for the Eagles.
The New Zealand-born player had a scan on the injury and did not travel to Japan.
Speaking at Ireland's base in Tokyo on Tuesday, skills coach Richie Murphy confirmed that Carbery was facing at least a month out of action.
"As far as I know it's a either a grade two or a grade three ankle sprain but he's going to be off his feet for a couple of weeks," said Murphy.
"The medical staff say he'll be ready to train in four to five weeks' time."
Leinster fly-half Joey Carbery has been ruled out of Ireland's two Tests in Japan because of an ankle injury.