TOKYO—An underdog wrestler won Japan’s summer sumo tournament, but it was a new trophy presented after the final match that stole the show.

President Trump on Sunday became the first American president to personally award a sumo wrestler with a prize, handing the 4 1/2-foot-high “President’s Cup” to 25-year-old victor Asanoyama before a crowd of 11,500. The arena erupted into cheers and applause when the white draping around the trophy was removed, revealing an eagle on top.

The event, part of Mr. Trump’s four-day visit to Japan’s capital to meet the country’s newly enthroned Emperor Naruhito, jolted the tradition-bound world of sumo, which is already facing an identity crisis. Foreign wrestlers have dominated the sport in recent years and matches are drawing more curious tourists, to the chagrin of some die-hard local fans.

Mr. Trump’s presence, itself a novelty, brought with it other novelties. The president didn’t watch the match sitting cross-legged on a zabuton floor cushion, as is the custom. Instead, he and first lady Melania Trump were offered chairs in a VIP box not far from the ring.

When it was time for prizes, stadium officials set up a staircase next to the raised sumo ring, which Mr. Trump and Prime Minister Shinzo Abe used to climb into the ring. Normally dignitaries have to scramble up unaided.