The contest will be part of a planned six-month campaign set to open April 1 and conclude October 3 ahead of the playoffs and World Series.
"I can't imagine how emotional and how powerful of an event that will be," Yankees manager Aaron Boone said.
The 2021 program was announced two weeks before the coronavirus-delayed 2020 MLB campaign is set to begin at empty home team stadiums, a campaign trimmed to 60 games per club opening nearly four months after the planned start of a 162-game season.
Two decades after planes were crashed into the World Trade Center and Pentagon and nearly 3,000 people died in New York and Washington attacks, the Mets will share the field with the Yankees, who reached the 2001 World Series only to lose to Arizona in seven games.
"I would imagine, especially, all that we've gone through this year maybe adding another layer of just how potentially powerful and emotional of a game and a day and an event that might be," Boone said.
"It's something that hopefully we're all a part of, and it will get the magic it deserves."
The Mets, who in 2001 played the first professional sports game in New York after the attacks, will play at Yankee Stadium over the July 4 US Independence Day weekend in 2021.
Every MLB club is scheduled to play next April 1. It could mark the first time since 1968 that every MLB team plays its season opener on the same day.
The 91st MLB All-Star Game is set for July 13, 2021, in Atlanta. This year's game scheduled for Los Angeles was canceled due to the virus outbreak.