Fans holding tickets for the original dates can use them at the new shows, or alternatively seek a refund through their original point of purchase.
The announcement was shared just hours before Sir Tom was due to take the stage at the Greek Theatre in Los Angeles, with the venue itself among those sending messages of support.
Fans were quick to rally around the veteran performer beneath his Instagram post, with one fan typing: “So very sorry to hear, Sir Tom. The main thing is you take care of yourself for once, get well soon. We, your fans, will always be there for you; we love and adore you.”
Elsewhere, a second echoed: “So sorry to hear this, Sir Tom. Wishing you a very speedy recovery. Take care of yourself, get plenty of rest. Your health is the most important thing.”