"I'm sincerely sorry to disappoint our audience, and thank you for understanding," he said.
A statement issued on his behalf said Joel's condition "has been exacerbated by recent concert performances, leading to problems with hearing, vision and balance".
It continued: "Under his doctor's instructions, Billy is undergoing specific physical therapy and has been advised to refrain from performing during this recovery period.
"Billy is thankful for the excellent care he is receiving and is fully committed to prioritising his health.
"He is grateful for the support from fans during this time and looks forward to the day when he can once again take the stage."
NPH is described by the NHS as an uncommon and poorly understood condition that most often affects people over the age of 60.
As well as the two UK dates, he had been due to perform in the US and Canada between this July and July 2026.
He had previously postponed shows in March because of a "medical condition", which was not specified at the time, "to allow him to recover from recent surgery and to undergo physical therapy".
Joel has regularly been on tour in recent years, and ended a record-breaking decade-long monthly residency at Madison Square Garden in New York last year.
He has been nominated for 23 Grammy Awards, winning five times, and was inducted into the Rock And Roll Hall Of Fame in 1999.
