The game was rescheduled as part of a day-night doubleheader Tuesday.
"It's a very emotional day. An extremely horrific act happened very near to the ballpark," Nationals General Manager Mike Rizzo said. "Our thoughts and prayers go out to all the victims over there and all the people affected by this. We felt it was inappropriate to play a major league baseball game with such tragedy right down the street."
One of the stadium's parking lots was used for families of the Navy Yard employees to meet after the evacuation of the facility.
The postponement was announced shortly after 3 p.m., about four hours before the scheduled start.
With some streets north of the stadium closed, there was heavy traffic on South Capitol Street, parallel to the third base line. Potomac Street, parallel to the first base line, was blocked by police. Police activity was visible around the stadium, and sirens could be heard throughout the afternoon.
Players from both teams were in the clubhouses at the time of the postponement along with stadium employees.
The doubleheader will open a three-game series. The Braves have a 10-game lead over second-place Washington in the National League East, and the Nationals began Monday 41/2 games behind Cincinnati for the final NL wild-card berth.
Pitching prospect to start for Royals
Top pitching prospect Yordano Ventura will make his major league debut for the Kansas City Royals on Tuesday night when he takes Danny Duffy's place in the rotation against Cleveland.
Duffy has been experiencing inflammation in his surgically repaired left elbow, and the Royals decided to give Ventura the start in a crucial series with playoff implications.
The Royals were 31/2 games behind front-runners Texas and Tampa Bay in the American League wild-card standings before Monday night's series opener against the Indians. Cleveland was half a game back of Texas and Tampa Bay.
Ventura was 5-4 with a 3.74 earned-run average at triple-A Omaha, helping the Storm Chasers win the Pacific Coast League championship.
Jhonny Peralta is expected to leave for the instructional league this week so he can keep working toward rejoining the Detroit Tigers after completing his 50-game suspension.
Manager Jim Leyland said Peralta will leave Wednesday for the instructional league in Florida, where he'll play in the outfield.
Peralta was Detroit's starting shortstop, but the Tigers acquired Jose Iglesias from Boston just before Peralta was suspended after baseball's investigation into Biogenesis of America, a Florida anti-aging clinic accused of distributing banned performance-enhancing drugs.
General Manager Dave Dombrowski has said that if Peralta returns, it won't be as the team's starting shortstop.
Leyland didn't want to speculate on whether Peralta would be part of the roster if the Tigers reach the postseason.