"Our advertising policies do not allow nudity or implied nudity but we have an exception for statues. Therefore, the ad with this image should have been approved," a spokeswoman for Facebook told AFP.
"We apologise for the error and have let the advertiser know we are approving their ad," she added.
The controversy began in December when Italian arts activist Laura Ghianda posted a picture of the artwork on the social networking site which went viral.
After it was censored she said that "this statue is not 'dangerously pornographic'. The war on human culture and modern intellectualism will not be tolerated."
Her outrage was echoed by Vienna's Natural History Museum, where the statue is displayed.
"Let the Venus be naked! Since 29,500 years she shows herself as prehistoric fertility symbol without any clothes. Now Facebook censors it and upsets the community," the museum said in a statement.
The 11-centimetre (4-inch) statue was discovered in the Austrian village of Willendorf in the early 20th Century.
It dates from the early stone age and is "the most popular and best-known prehistoric representation of a woman worldwide," according to the museum's director general Christian Koeberl.
Facebook is regularly criticised over content which it bans or indeed content it allows to be published.
On March 15, a French court is due to pronounce on the decision by the California-based social networking site to close the Facebook account of someone who posted a photo of 19th century French painter Gustave Courbet's "Origin of the World" painting, which depicts female genitalia.