The singer was due perform in memory of those affected by the attack - which took place at her concert.
Geoff Taylor, chief executive of the Brit Awards, said she was unable to travel "on doctor's orders".
Ariana later posted on her Instagram story a video of Liam Gallagher performing Live Forever in tribute.
Twenty two people died in the bombing at Manchester Arena on 22 May.
"We think it's really important to recognise that terrible atrocity and the impact on so many lives so I can confirm we did have Ariana Grande lined up to make a performance tonight," Geoff said.
"Unfortunately she was not able to travel on doctor's orders, she's not well, and I can say that there will be something tonight, I can't say any more than that but people should tune in and watch.
"And hopefully it will be a fitting remembrance and recognition of what happened, which was so terrible."
Liam Gallagher stepped in for Ariana and performed Oasis' Live Forever.