The TV star, 51, was due to be one of the hosts of the charity show tonight (18 March) but has tested positive for COVID.
Ball told fans on Twitter: "Pook!
"Fell at last hurdle and have had positive lat flows this am - noooooooo - gorgeous @AleshaOfficial is going to work the double shift tonight on @ComicRelief, I owe you lady love - good luck to A, Lenny, David, Paddy, AJ, Vernon, & the @comicrelief gang."
"There are so many brilliant treats in store tonight," she went on.
"I'll be watching & supporting from bed (probably in full make up, outfit, heels and all) might invite @joeldommett over #sickbay."
Minogue had been due to take part in a sketch with the cast of BBC sitcom Ghosts, but said she wouldn't be able to as she was recovering from COVID.
"So sorry to miss my planned visit to #BBCGhosts Button House for #ComicRelief2022 as I’ve been recovering from COVID," she tweeted.
"I WILL, however, be watching @BBCOne 7pm Friday to see what fun @comicrelief has in store for us! Don’t forget to tune in & support the incredible work they do!"
Dommett was also lined up to host and is being replaced by Vernon Kay, who he quipped was "better looking" and "more talented".
"Super annoyed to report that I have the vid," he posted on Instagram.
"This unfortunately means I have to pull out of hosting @comicrelief... My incredible replacement is the better looking, more talented @vernonkay who is ace.
"I’ll be watching from home donating loads of money like everyone else!"
Comic Relief will see Dawn French and Jennifer Saunders reprise their characters The Extras in a sketch show version of The Repair Shop, and Strictly Come Dancing winners Rose Ayling-Ellis and Giovanni Pernice will perform a waltz.
Comic Relief's main night of programming airs on Friday, 18 March from 7pm on BBC One.
Watch: Tom Daley discusses gruelling Comic Relief trek