Creed star Jordan was unveiled as the 2020 recipient of People Magazine's annual award on Jimmy Kimmel Live! (17 November)
Johnson mocked the president by jokingly refusing to concede while posting a photo of himself as the 2016 winer.
“Congrats to my brother @michaeljordon on the new sexy crown,” he wrote on Instagram. “I CONCEDE NOTHING.”
Johnson was poking fun at Trump for refusing to accept defeat at the hands of President-elect Joe Biden, whom the actor supported at the 2020 US presidential election.
Trump has repeatedly made unfounded claims of electoral rigging and has threatened legal action.
Speaking to People about winning the award, Jordan joked that the women in his family “are definitely proud of this one”.
Previous winners of the award include John Legend and Idris Elba.