Dowsett was set to target the record, which he has held previously, on Manchester on December 12.
A new date for the attempt has not been set but Dowsett confirmed it will be in 2021.
"I am really disappointed the attempt can't go ahead as planned but my health is first and foremost the priority," Dowsett said in a statement from the UCI.
"I'd like to thank everyone, the event organisers, event sponsors, my team, the UCI and above all the public for their support and very much look forward to attacking the record in 2021 with the same intent. We're looking to announce a 2021 date as soon as possible."
The setback comes as a major blow, given the British rider had hoped to use the form acquired through the Giro d'Italia, where he won a stage. He described the three-week races as "a phenomenal training block" but will now have to adjust his approach.
Dowsett revealed his plans to target the UCI Hour Record last week, saying he wanted to try and take it back before he ran out of time in his career.
The 32-year-old broke the record back in 2015, covering 52.937km, but it was soon toppled by Bradley Wiggins, while Victor Campenaerts last year raised the benchmark again to 55.089km.
Dowsett has acknowledged that Campenaerts' distance will be tough to beat, but that his 2015 effort didn't fulfil his true potential.
"Last time around we got the record but it was deeply frustrating because we realised that there was quite a lot left in the tank," he told Cyclingnews. "To put all that work in and then deliver an 80 per cent ride was frustrating, so I want to see what I'm capable of."
Dowsett, who will ride the event in support of awareness of the haemophilia condition he suffers from, revealed he wanted to have another go at the record for a while, but has only now found the right opportunity.
Today's best Black Friday deals
Today's cycling-related highlights from the Black Friday sales. For even more, view our guide to the best Black Friday bike deals where you'll find on all things cycling, including bikes, helmets, clothing and more.
Today's best deals: USA
- Competitive Cyclist: 66% off Assos S.J.Blitzfeder rain jacket
- Rei: Cannondale Topstone Ultegra RX 2
$3,300.00| $2,804.73 | 15% off
- Jenson USA: Giro Empire ACC shoes
$300.00| $104.99 | 65% off
- Chain Reaction Cycles: LifeLine 18-piece tool kit
$73.99| $49.99 | 32% off
- Velocio: Signature Softshell jacket with 40% off
- ProBikeKit: Continental GP5000 road tyre
$79.49| $47.99 | 39% off
- Wiggle: Fizik R4B Road Shoes
$200.00| $114.00 | 43% off
Today's best deals: UK
- Wiggle: Garmin Edge 1030 cycling computer with 40% off
- ProBikeKit: 300-lumen rear Lezyne light for under £35.00
- Tredz: Blackburn Mag 5 turbo trainer | was £139.99, now £125.99 | 10% off
- Chain Reaction Cycles: Endura MTR Shell Jacket
£139.99| £76.99 | 45% off
- CycleStore: Over 60% off Specialized, Endura, Pearl Izumi and more
- Rutland Cycling: 36% off Moon Storm & Nebula lightset
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