He sustained the injury during Argentina's 1-0 victory against Colombia on Sunday (Monday AEST) in the Copa America final in Miami.
"After a medical evaluation, it has been determined that Leo Messi has suffered a ligament injury in his right ankle," Inter Miami said in a statement on Tuesday (Wednesday AEST).
"The captain's availability will be determined by periodic assessments and the progress of his recovery."
Inter Miami coach Gerardo "Tata" Martino said earlier on Tuesday, before the test results, that Messi was expected to miss at least two matches.
"He twisted his ankle, and the injury is present so tests are needed and (we) wait for results," Martino told reporters.Â
"I've had the opportunity to see other images. There will be tests done to determine the severity of the situation.
"We are always informed through our kinesiologist Walter Insaurralde, who is also the kinesiologist of the national team. He is very cautious at giving a final diagnosis before results are in."
Inter Miami are second in the Eastern Conference standings heading into home matches this week against Toronto FC on Wednesday and the Chicago Fire on Saturday.
Messi, 37, has scored 12 goals and 13 assists in 12 MLS matches this season, the eight-time Ballon d'Or winner's first full campaign in the league.
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