The Holland international sent out a mocked-up picture of the World Cup final referee wearing a Manchester United shirt following his side's 1-0 FA Cup third-round defeat at Old Trafford.
Babel also wrote: "And they call him one of the best referees? That's a joke. SMH (shaking my head)."
The 24-year-old later added: "My apology if they take my posted pic seriously. This is just an emotional reaction after losing an important game. Sorry Howard Webb."
The apology has not been enough to prevent a charge from the FA, who said in a statement: "The charge relates to comments and images published by the player on Twitter concerning referee Howard Webb."
Babel has until 4pm on Thursday to respond to the charge.
Liverpool manager Kenny Dalglish said earlier he felt it was just a joke and had hoped further action would not have been necessary.
"Maybe I've been out of the game too long but let's see if they can find a sense of humour," he said.
"He apologised straight away."
And Dalglish joked: "I don't think he's clever enough technically to have drawn that up himself."