ABC News reportedly announced "we all agreed it’s best for everyone that they move on."
Holmes' divorce filing from his wife comes nearly a month after photographs published in the Daily Mail revealed a relationship with Amy Robach.
News division President Kim Godwin said she needs time to "work through" what's best for the organization.
On Friday's show, the two seemed to reference the hubbub that started on Wednesday after the Daily Mail published photos of them together.
“It is clear that ABC News’ enabling of Mr. Epstein has consequences," the House minority leader wrote to the network's president.
The journalist spoke to Ashley Bianco, a CBS producer who was fired after the network learned she had access to Amy Robach's interview with Virginia Giuffre.
The "20/20" host has since spoken out, calling it "a private moment of frustration" and stating her reporting didn't meet editorial standards.
Amy Robach posted the 2015 interview on Tuesday, calling Fisher "brilliantly talented and funny."