Facebook said that Yu, who joined the company from Google in 2007, will be leaving but did not comment on the reasons for his departure.
Its official statement said: "Gideon has played an important role in helping us to achieve our financial success, building a strong finance team and establishing the core financial operations of our company.
"Despite the poor economic climate, we are pleased that our financial performance is strong and we are well positioned for the next stage of our growth. We have retained Spencer Stuart to lead our search for a new CFO and will be looking for someone with public company experience."
Facebook also released some financial details for the first time in what was seen as an attempt to dampen reports that it needs to raise extra capital.
The company, which has almost 200m registered users, said that it expects revenue to be up 70% in 2009 from 2008 and that it will reach profitability in 2010.
Various commentators and tech blogs have described Facebook's hunt for a CFO with "public company experience" as a clear sign it is moving toward an IPO.
Mashable said it "would set the stage for an IPO", while Barron's Tech Trader Daily said: "Here comes the IPO."