Springsteen and his E Street Band had played Sunderland's Stadium of Light on Wednesday, later describing the weather as ":hellacious".
The star was honoured at London's Ivor Novello Awards on Thursday, treating the audience to his song Thunder Road, after Sir Paul McCartney presented him with his Ivors Academy fellowship.
He was previously named the first international songwriter to be inducted into the fellowship before the ceremony took place.
On Saturday, he was forced to postpone a date at Marseille "due to vocal issues", and an Instagram post on his account said "further examination and consulting has led doctors to determine that Bruce should not perform for the next 10 days".
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His European stadium tour is now set to resume on June 12 in Madrid.
"Additional postponements are required for Airport Letnany in Prague (originally scheduled for May 28) and San Siro Stadium in Milan (originally scheduled for June 1 and 3)," the statement also said.
"New dates for these shows will be announced shortly.
"Bruce is recuperating comfortably, and he and the E Street Band look forward to resuming their hugely successful European stadium tour on June 12 in Madrid at the magnificent Civitas Metropolitan."
Springsteen previously rescheduled dates in the US last year after being taken ill and over other issues cancelled planned concerts in March 2023.
His first major tour in six years saw him play a headline gig in London's Hyde Park in July 2023.
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