WASHINGTON—President Trump said on Monday that he intends to present golfer Tiger Woods with the nation’s highest civilian award, the presidential Medal of Freedom, following his dramatic win at the Masters.

Mr. Trump, an avid golfer himself, announced his intention to grant the award to Mr. Woods in a Twitter message while flying to Minnesota.

“Spoke to @TigerWoods to congratulate him on the great victory he had in yesterday’s @TheMasters, & to inform him that because of his incredible Success & Comeback in Sports (Golf) and, more importantly, LIFE, I will be presenting him with the PRESIDENTIAL MEDAL OF FREEDOM!” he said.

On Sunday, Mr. Woods rallied from behind to win his fifth career green jacket on Sunday at Augusta National Golf Club. It marked his 15th major victory and first since the 2008 U.S. Open. It capped one of the greatest career revivals in the history of sports.

Mr. Trump has occasionally golfed with Mr. Woods. In February, the two men played with Jack Nicklaus, who currently holds the record for the most golf majors at 18.