The Israel Start-Up Nation rider had planned an assault on the prestigious record at the Manchester Velodrome on December 12, but the event has been halted after Dowsett contracted coronavirus.
Dowsett said he is "really disappointed" by the news, but said he will focus on his isolation and recovery, with his attempt now postponed until next year.
The 32-year-old pro from Essex said: "I am really disappointed the attempt can’t go ahead as planned but my health is first and foremost the priority.
"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.”
Dowsett added on Twitter: "Really disappointed to have to postpone the Hour Record attempt. Shortly after we announced the attempt I had some symptoms of Covid and a test result came back positive.
"My focus now is recovery, isolation & my health. Thanks to everyone for their support, we’ll be back stronger."
Dowsett had planned to take back the prestigious title, which he briefly held in 2015 before Sir Bradley Wiggins beat his distance a month later.
The current record is held by Belgium's Victor Campenaerts, who set a staggering 55.089km benchmark in 60 minutes in April 2019.
NTT Pro Cycling rider Campenaerts set his record at 1,800 metres above sea level at the Aguascalientes velodrome in Mexico.
Dowsett had been training hard to prepare for his record attempt, putting up some big distances around his home county Essex in November.
Camenpaerts says Dowsett has a 50 per cent chance of breaking his record and added that he would try to retake the title if Dowsett is successful.
A new date for Dowsett's attempt has not yet been set.
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