The museum piece, which has drawn criticism from Christian leaders who say it's disrespectful, was damaged Sunday when a male visitor pushed over the figures of the Beckhams before running out, museum spokeswoman Diane Moon said.
The exhibit had been closed off and police and museum staff were investigating security footage to track down the vandal, Moon said.
The waxwork tableau also features President Bush, British Prime Minister Tony Blair and Prince Philip as the three Wise Men; actors Hugh Grant and Samuel L. Jackson as shepherds; and disco diva Kylie Minogue as an angel.
The display drew the ire of church leaders when it went on show last week.
"To have a very special part of Christianity depicted in this way and its most precious symbol, which is the coming of God into the world in Jesus Christ, seems to me to be not just disrespectful to Christians, it is also disrespectful to the heritage of Britain and also does damage to the culture of this country," the head of the Roman Catholic church in England and Wales, Cardinal Cormac Murphy-O'Connor, tells the BBC.
A Vatican spokesman said it was unacceptable to have celebrities representing Jesus, Joseph or Mary.
The Rev. Jonathan Jenkins, spokesman for the archbishop of Canterbury, who leads the world's 77 million Anglicans, said the depiction went too far.
Moon said the nativity scene had been an incredibly popular exhibit and museum staff hoped to have it back on display as soon as possible.
"We are assessing the damage now, we don't know if it's going to be repairable in a day or if it will take longer," she said.
She said the museum had received about 70 complaints about the exhibit.
"The vast majority of people have taken it in the spirit in which it is intended — a bit of festive fun," she said.