It comes one day after the McFly singer and his professional dance partner made their debut on the first live show of the BBC series.
The pair are now self isolating separately and will miss the next live show on Saturday.
A BBC spokesperson said in a statement: “While they will both miss Saturday’s live show, Strictly Come Dancing protocols mean that, all being well, they will return the following week.”
Fletcher, 36, and Dowden, 31, will not be able to practice together for 10 days, and Fletcher will miss McFly’s next tour performance on Sunday night.
The singer said he is “so, so sorry” to miss the gig and his band will perform without him at The SSE Hydro arena in Glasgow.
It follows a reported vaccine dispute behind the scenes where it is believed that three professional dancers have refused to be vaccinated.
Amy, who has Crohn’s disease, said she was vaccinated on February 4 in an Instagram post.
On Saturday, Fletcher and Dowden performed the cha cha to September by Earth Wind and Fire.
The following day, McFly confirmed on social media that Fletcher had to pull out of the band’s concert in Scotland after falling ill.
A statement read: “Unfortunately Tom is unwell and won’t be onstage with us tonight in Glasgow.
“He sends huge and heartfelt apologies to all the fans he won’t see tonight.
Unfortunately Tom is unwell and won't be onstage with us tonight in Glasgow. He sends huge and heartfelt apologies to all the fans he won’t see tonight. The show will still be going ahead, we’re looking forward to seeing you all and need you guys to sing extra loud for us tonight pic.twitter.com/yyUpavdYcy
— mcfly (@mcflymusic) September 26, 2021
“The show will still be going ahead, we’re looking forward to seeing you all and need you guys to sing extra loud for us tonight.”
The band later confirmed that Fletcher had tested positive for Covid and wished him a speedy recovery.
Strictly Come Dancing has seen its television audience grow to almost eight million viewers, according to overnight ratings for Saturday.