Both TV shows are said to have pulled MJ's back catalogue from being performed on their respective new series later this year.
It follows documentary film Leaving Neverland: Michael Jackson and Me, which detailed claims from two men who alleged they had been sexually abused by Michael Jackson.
A source told The Sun newspaper of the BBC's decision: "In light of the recent allegations there is concern viewers might be deterred by any reference to Michael Jackson, which has caused a lot of distress for some viewers, and want to ensure their audience has an enjoyable time watching.
“It is also feared dancers performing to an MJ track could be at a voting disadvantage. It seems the safest decision.”
A spokesperson for the BBC told the tabloid: "We consider each piece of music on its merits and decisions on what we play on different networks are always made with relevant audiences and context in mind.”
The X Factor is set to also drop use of Jackson's songs for its upcoming series in the autumn, according to The sun.
The news comes as a number of radio stations also stopped playing Michael Jackson's songs while a statue of the singer has been removed from the National Football Museum in Manchester.
The estate of the late Michael Jackson previously branded the allegations in the documentary "dated" and and "discredited".
They said in a statement to TMZ: "This is yet another lurid production in an outrageous and pathetic attempt to exploit and cash in on Michael Jackson."
Relatives of Jackson have also defended him against the claims.
The singer's nephew, Taj Jackson, told Reuters: "This is the 10-year anniversary of my uncle's death. We should be mourning, but instead we are being bombarded with lies."