The Liverpudlian singer-songwriter, responsible for hits such as Alison, Oliver’s Army and I Can’t Stand up For Falling Down, announced on social media he was postponing Sunday’s Portsmouth show and Monday’s in Swansea.
His current tour is in support of The Boy Named If, his first album to crack the top 10 since 1994’s Brutal Youth.
The Guildhall show was close to being sold out, but is expected to be rescheduled.
The statement said: ‘Unfortunately, Elvis Costello and The Imposters have to announce the postponement of their dates in Portsmouth and Swansea as Pete Thomas is indisposed.
‘We apologize to our friends in Pompey and Swansea and will look forward to seeing you all again when we can.
‘It is hoped that the greatest rock and roll drummer in the world will return to the stage later this week, as soon as he is recovered.
‘Stand by for action.’