He pulled out of a performance at Stansted Park on Wednesday due to being unwell.
A statement posted on the singer's official Twitter account on Thursday read: "It is with regret that we have to postpone Tom Jones' performance at Chester Racecourse this evening.
This show will be rescheduled for Sunday 12th August.
"Sir Tom Jones has a bacterial infection for which he is being treated in hospital.
"The condition is being well managed and we are hoping for a speedy recovery. He is extremely sorry and disappointed not to be able to perform tonight, and sincerely apologises for inconveniences caused to the audience and all those who are involved in the event."
Sir Tom has issued a follow-up statement, apologising for cancelling the two gigs and thanking his fans for their "support and understanding".
In a post on Twitter, he said: "I am so sorry for cancelling last night's show in Chichester, it's the worse feeling having to let down everyone who was coming as well as everyone who is involved in the event.
"I know many of you travel considerable distances and make plans with friends and family that take a lot of effort, and it is so disappointing when things don't go right.
"Although I can't perform again tonight at Chester Racecourse, the good news is that we can get another date in Chester on August 12, so hopefully I will see you there. Until then, a sincere thank you for your support and understanding."