Trump, who has been critical of Cook, has claimed that she should be fired for not handling her mortgage applications correctly.
Cook filed the lawsuit on Thursday with a federal court in Washington, according to court records. The contents of the entire lawsuit were not immediately available, reports news agency Bloomberg.
This is another step in the sharply escalated conflict between the White House and the Fed. Not least, Fed Chairman Jerome Powell has been in the line of fire for Trump's attacks.
The central bank has resisted the president's increasingly loud demands to lower interest rates and has stubbornly argued that monetary policy decisions should be made based on real economic statistics and without political interference.
If Cook is forced to interrupt her term prematurely, a vacancy is created in the Fed's board of directors. Donald Trump could use this to get a more favorably inclined member in.
Lisa Cook was nominated in 2022 to her current position by former President, Democrat Joe Biden.
