The former Beatle is expected to make a full recovery after being treated in a Japanese hospital for a viral infection.
McCartney, 71, was forced to pull out of concerts in Japan and South Korea earlier this week.
However, a spokesperson for the musician has said that the star is doing well and will be back to full health soon.
In a statement, spokeswoman Perri Cohen 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. Paul has been extremely moved by all the messages and well wishes he has received from fans all over the world."
Sir Paul, who is currently on a world tour, is said to have been "extremely moved" by the messages of support he has received.
The musician's next scheduled show is in Lubbock, Texas, USA, on June 14.