The agency asked the drug maker, AstraZeneca, to "immediately cease the dissemination" of the ad.
AstraZeneca had no immediate response to the request.
"The 'patient safety' print ad makes false or misleading safety claims that minimize the risks associated with Crestor, thereby suggesting that Crestor is safer than has been demonstrated by substantial evidence or substantial clinical experience," the FDA said in a letter dated Tuesday.
The advertisement in question appeared in The Washington Post on Nov. 23, prompting Dr. Sidney Wolfe of the consumer group Public Citizen to complain to the FDA. Wolfe has sought to have Crestor withdrawn because of its rate of liver problems.
Crestor is one of a group of medications called statins that are used to lower cholesterol. Crestor's prescribing information includes warnings about side effects including possible liver damage or failure.
Facing criticism for drug safety lapses, the FDA is cracking down, reports CBS News Correspondent Barry Bagnato.
In its complaint the FDA took issue with claims that FDA scientists have confirmed that concerns about the safety of the drug have no basis.
The agency has published no statement on its Web site saying the concerns about Crestor have no basis, the FDA said.
In addition, the agency said, "recent public statements made by the agency contradict that conclusion."
The FDA letter noted a recent statement by Dr. Steven Galson, its acting director for drug evaluation and research, that the agency "has been very concerned about Crestor since the day it was approved, and we've been watching it very carefully."