The accusation against the film and TV star originated from a string of now-deleted tweets, which were shared or discussed by other people on Twitter despite their seemingly baseless nature.
In March, Oprah was the victim of a similar conspiracy theory, and spoke out against the “awful” and “fake” report that her home had been raided by police.
A producer on Ellen DeGeneres’ talk show, Andy Lassner, was among those who tried to point out the post was false when it went viral.
“The staggering amount of people believing a 100 per cent fake story about Oprah doesn’t make me feel good about the chances of society continuing,” he wrote.
Duff urged the person who started the rumours about her to “get a hobby” and “take a break from their phone” in a post from her official Twitter account.
“Everyone bored af right now I know..but this is actually disgusting….. whoever dreamed this one up and put this garbage into the universe should take a break from their damn phone,” she wrote.
“Maybe get a hobby.”