Mudd is one of six former executives at Fannie, the Federal National Mortgage Association, and Freddie Mac, facing civil fraud charges from the Securities and Exchange Commission.
The executives are accused of understating the level of high-risk subprime mortgages that Fannie Freddie held just before the housing bubble burst.
Fannie and Freddie have cost taxpayers more than $150 billion to date — the largest bailout of the financial crisis. Regulators say that tab could hit $259 billion.
The companies have since essentially become wards of the state.
Legal experts say they don't expect the executives to face criminal charges, however, the SEC took action amid widespread criticism that no one was being held accountable for a financial crisis that reached across the globe.
The SEC has agreed not to charge Fannie and Freddie. The companies, taken over in 2008, have agreed to co-operate in the case against the former executives.
Randal Nardone, principal and co-founder of the hedge fund, Fortress Investment Group, will serve as interim CEO in Mudd's absence.
"I have requested a leave of absence from my position as chief executive officer to ensure that any time or attention I need to focus on matters outside of Fortress will not affect the business or operations of the company," Mudd said.
Mudd, 53, was leading the mortgage giant in 2007 when it became clear that the housing market began to disintegrate.
Investigators say that executives at the Fannie and Freddie mislead the public, and investors, in congressional testimony, as well as in reports and speeches.
Fannie Make was established by the government in the 1930s to encourage homeownership by buying mortgages from banks. That freed cash for the banks so they could make new loans.