According to US media reports, Republican Congressman Thomas Massie of Kentucky introduced the resolution, accusing Defense Secretary Hegseth of mishandling the US war against Iran.
The resolution is expected to face a vote in the House of Representatives by Wednesday, November 11, according to the report.
The move has attracted attention because the impeachment resolution was introduced by a member of Hegseth's own Republican Party, which has largely supported the Trump administration.
Massie, who represents Kentucky in the House of Representatives, has raised concerns over Hegseth's handling of the military conflict with Iran and the decisions surrounding US military operations.
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Before the resolution was introduced, Hegseth had publicly defended President Donald Trump's decision to launch military action against Iran, saying he supported the decision and would make the same choice again.
The development comes amid growing political debate in Washington over the US military campaign against Iran and the role of the Defense Department in overseeing military operations.
However, introducing an impeachment resolution does not automatically remove a Cabinet secretary from office. The resolution must first secure approval from the House of Representatives before further constitutional proceedings can take place.
The move could add to political pressure on the Trump administration as lawmakers debate the legal and strategic implications of the US conflict with Iran.