Story highlights "When I learned of her status, we immediately ended her employment," Puzder said

Puzder is the head of the parent company that owns fast food companies Hardee's and Carl's Jr.

(CNN) Andrew Puzder, President Donald Trump's pick to lead the Labor Department, employed an undocumented immigrant for years, the business magnate said in a statement Monday. It's an admission that in the past has sunk other Cabinet secretary nominees.

Puzder's nomination has been stalled in Congress after a series of delayed hearings from the Senate Committee on Health, Education, Labor and Pensions. Puzder, the head of the parent company that owns fast food companies Hardee's and Carl's Jr., said he and his wife have already paid back taxes on the employee.

"My wife and I employed a housekeeper for a few years, during which I was unaware that she was not legally permitted to work in the US," Puzder said in a statement. "When I learned of her status, we immediately ended her employment and offered her assistance in getting legal status."

He added: "We have fully paid back taxes to the IRS and the state of California and submitted all required paperwork."

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