The 72-year-old was due to perform Saturday in Hyde Park in London in a concert associated with the Olympics and Sunday at the Osborne House on the Isle of Wight, the BBC reported.
Jones took to Twitter to apologize to fans, explaining the cancellations were on "doctor's orders."
British singer-songwriter Will Young replaced Jones Saturday at the free London concert.
"I'm sad that Tom Jones can't do the show, I hope he gets well soon, and am very happy and excited to be playing Hyde Park for the Olympic events tomorrow," Young said Friday.
Ticket holders for the Isle of Wight show will be refunded, organizers of the event said.
"We are very sorry for any inconvenience this might bring, and appreciate your understanding," the said. "We wish Tom Jones a quick and full recovery."