The entertainment site TMZ first published video on Tuesday capturing the exchange, and the White House did not dispute its authenticity.
"A lunatic was wildly screaming expletives in a complete fit of rage, and the President gave an appropriate and unambiguous response," White House spokesman Steven Cheung told Reuters in an email.
Trump was touring the Ford F-150 assembly facility in Dearborn when a worker on the plant floor shouted what sounded like "pedophile protector" as the president stood on an elevated walkway, the video showed.
Trump turned toward the individual and appeared to respond with an expletive before making a hand gesture with his middle finger as he walked off.
Other Ford employees cheered and welcomed the president as he toured the assembly line, taking photos with workers and shaking hands.
Trump has occasionally used profanity in public settings, often in response to criticism, confrontation or to emphasise his point.
He has faced persistent scrutiny for his handling of sensitive federal records tied to Epstein, a convicted sex offender who died by suicide in jail in 2019.
Many of Trump's most loyal supporters believe the government is withholding documents that would reveal the late financier's ties to powerful public figures.
He has repeatedly denied any knowledge of Epstein's alleged abuse and sex trafficking of girls and has not been accused of wrongdoing.
Trump's visit to the Michigan facility was part of an effort to highlight his administration's support for US manufacturing, a key theme as the 2026 election year unfolds.
Michigan is seen as a politically important state, and domestic jobs and industry have been central to Trump's economic messaging.
