The medical lab said Hagemann, who also serves as senior vice president, will stay through May 31, unless his successor is named and the transition takes place before then. Hagemann will help chose his successor.
Hagemann said in a statement that after almost 15 years as CFO, he and the company agreed that "now is a good time for a change."
Quest posted a 71 percent decline in earnings for the fourth quarter, which was effected by Superstorm Sandy.
The Madison, N.J., company also gave a 2013 earnings and revenue forecast that fell below Wall Street expectations.
Quest shares have slipped 4 percent so far in 2013, after closing Wednesday at $55.99.