Paul McCartney, 71, has postponed five shows in Japan and South Korea.
A statement said: “Since contracting a virus last week that led to the postponement of tour dates, Paul received successful medical treatment at a hospital in Tokyo.
“He will make a complete recovery and has been ordered to take a few days rest.”
The statement added: “Paul has been extremely moved by all the messages and well wishes he has received from fans all over the world.”
Paul McCartney is in the middle of his Out There world tour, which has been on the road for more than a year.
It has already travelled through Japan once as well as visiting North and South America and parts of Europe.
Paul McCartney had been due to play four further concerts in Tokyo and Osaka, including one show at Tokyo’s Nippon Budokan Hall, where the Beatles performed on their first Japanese tour in 1966.
The former Beatle was then due to make his first trip to South Korea to perform at Seoul’s Olympic Stadium.
Paul McCartney’s tour is due to resume with 19 more dates in the US beginning in Lubbock, Texas, on June 14.
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