The Portugal forward has been granted more time off and will not be on the flight to Bangkok, which is due to leave Manchester at 4.30 p.m. U.K. time (11.30 a.m. ET) on Friday.
Sources told ESPN there is no timeframe for Ronaldo to rejoin the squad.
A statement from United said: "Cristiano Ronaldo will not be in the party departing for Thailand as he has been granted additional time off to deal with a family issue."
Ronaldo wants to leave Old Trafford this summer to join a club playing Champions League football next season. United insist the 37-year-old, who has a year left on his contract, is not available for transfer.
Ronaldo was due to return to Carrington on Monday but was given permission by the club to take an extended break for personal reasons. He returned to United from Juventus last summer and scored 24 goals in all competitions last season. But his form in front of goal could not prevent a sixth-place finish in the Premier League and failure to qualify for the Champions League.