McCartney -- one of two living members of The Beatles -- had already cancelled performances at the National Stadium in Tokyo on Saturday and Sunday, after coming down with the unspecified illness.
He "will regrettably have to cancel the remaining Japanese shows. Paul is still not feeling better and this cancellation is unavoidable," organiser Kyodo Tokyo said in a statement.
A company spokeswoman said the musician was "staying at a hotel in Tokyo and doctors are with him", but added that it was "unclear" if he would still perform at a South Korean concert scheduled for May 28.
The cancellation generated an outpouring of good wishes from fans of the Liverpool-born musician.
"Dear Paul, please take care of you! Our hope is only your perfect recovery," Mari Yamashita wrote in English on the tour's official Facebook page.
Another posting by Mami Siozaki said: "It's been 15 years since I became a fan of The Beatles. I was looking forward to a concert on Saturday... I wish you regain strength and come back soon."
McCartney had planned to play at another venue in Tokyo on Wednesday and the last one in Osaka on Saturday as part of his "Out There" world tour.
There were also plans for a Monday show to make up for the cancelled Saturday event. In all, McCartney had been expected to play in front of about 170,000 fans in Japan during the four-date tour, according to public broadcaster NHK.
- 'Hugely disappointing' -
Among McCartney's Tokyo dates was a show at the Nippon Budokan Hall, which would have marked his first return to the venue since appearing there with The Beatles in 1966.
"I was really looking forward to playing in Japan again after we had such an amazing time here in November," McCartney was quoted as saying in the statement.
"So, to cancel these shows as well as the National Stadium shows is hugely disappointing for me as well," he said.
"I'd like to thank my Japanese fans for their love, messages of support and understanding. I hope to see you all again soon. Love, Paul," he added.
In an earlier tour of Japan in November last year, McCartney was seen singing 39 songs non-stop without retreating backstage.
Major-selling Japanese newspaper the Asahi, citing people familiar with the situation, said McCartney's condition was improving but that he was still too unwell to perform on stage.
Organisers were exploring "all possibilities" to reschedule the four-date Japan tour, they said.
The musician flew into Tokyo after a short rest at home in London following a strenuous South American tour.
The Nippon Budokan Hall show had set aside 100 seats for those 25 and under at 1,500 yen ($15) each, the same price as they were 48 years ago when The Beatles played the venue.
The rest of the tickets for the concert, originally scheduled for May 21, were priced at up to 100,000 yen.
Some comments on social media criticised organisers for the sudden cancellation and what they said was a slow refund process.
But Osaka resident Nariaki Shimizu brushed aside the criticism.
"I decided to keep my ticket for (the Osaka concert) without a refund, together with a ticket for the 1980 Nippon Budokan Hall", he wrote, referring to an earlier concert that was also cancelled.
In 1980, McCartney was arrested at a Tokyo airport for marijuana possession and was deported. That led to the cancellation of a Japan tour by Wings, the post-Beatles band fronted by McCartney.