His management made the announcement on Friday night, saying the issues are “beyond our control”.
The former Smiths frontman, 59, had been due to play two gigs at Castlefield Bowl in his home city of Manchester on 7 and 8 July.
Other shows had been scheduled for Reading, Portsmouth and Edinburgh in July.
A statement shared on Morrisey’s official Facebook page said: “Due to logistical problems beyond our control, the UK/European Morrissey concerts scheduled for July will be postponed.
“We deeply regret any inconvenience to the fans and promise to reschedule UK and European dates as soon as possible.
“All original purchasers from official ticket outlets will have the full ticket fee refunded including booking fee to their credit/debit cards. Refunds from ticket agents will be actioned from midday on Monday July 2.”
Morrissey’s management thanked fans for their support and said his world tour would continue in Mexico City on 23 November.
Morrissey’s manager, Peter Katsis, had earlier criticised the organiser of an anti-racism party in Manchester, which was due to take place at the same time as his concert and just around the corner.
Campaigners, who say they are former Morrissey fans, are holding the event after he made comments supporting jailed EDL founder Tommy Robinson.
In a statement, Katsis accused the event’s organiser, Dave Haslam, of being an attention-seeker and claimed the move was “bulls**t”.
Haslam, a former DJ at Manchester’s Hacienda nightclub, said: “I sympathise with fans who made plans to see him, we know what it’s like to be let down by Morrissey.
“If dates are rescheduled, we’ll be happy once again to provide an alternative event in the city. One that counters Morrissey’s support for Tommy Robinson and the far right.”
He added that the event will go ahead as planned, despite the Morrissey shows being cancelled.
Katsis, of Deckstar Management, previously called Haslam a “has-been”, claiming he was never a Morrissey fan and had an agenda.