In a tweet posted on Friday morning, Rayner, 39, said the symptoms began on Thursday evening and “have gradually got worse”.
The shadow education secretary is widely expected to easily win the race to succeed Tom Watson as Labour’s deputy leader.
The result is due to be announced on April 4.
The coronavirus pandemic has effectively frozen both the Labour leadership and deputy leadership campaigns.
Corbyn, who has one week left in the top job, told the BBC this morning the coronavirus outbreak proved he had been “absolutely right” about public spending at the 2019 general election.
The latest figures from the Department of Health, released on Thursday, showed a total of 578 people who tested positive for coronavirus in the UK have died.