The decision to overturn Lampard's sending-off was reached at a Football Association regulatory commission hearing.
"A claim for wrongful dismissal from Chelsea's Frank Lampard was upheld," said a statement on the FA's website.
"As a result, Lampard's three-match suspension has been withdrawn."
The news was welcomed by Chelsea manager Avram Grant.
"I think the decision is the right decision because even the referees
sometimes make mistakes, especially the assistant referees," said the Chelsea boss.
"It is not the first time. I think for the FA it is important to show when the
referee makes a mistake that the game is fair for everybody."