The latest announcement by police said that 13 people, including a suspected gunman, were killed and others were wounded after a man opened fire at the facility on Monday morning.
The Nationals took the decision to postpone the match in conjunction with Major League Baseball and will instead play a a day-night doubleheader on Tuesday.
"All of us here in the Nationals organisation were deeply saddened to learn of the tragic events that occurred this morning only a few blocks from Nationals Park," the team said in a statement on MLB.com.
"Our thoughts and prayers go out to the victims and their families.
"The safety of our fans is our utmost priority. As we have throughout the day, the Nationals security personnel will continue to work closely with all levels of law enforcement to reinforce the already high level of security in place at Nationals Park."
Nationals general manager Mike Rizzo added: "There are a lot of (logistics) that go into cancelling a game for these reasons.
"We have to be in contact with federal authorities and the state D.C. authorities to have a coordinated effort, and then whenever you cancel a game, MLB is involved and we have to go through the correct procedures for that."
Braves pitcher Scott Downs agreed that the match was rightly low down in everyone's priorities.
"Nobody is thinking about baseball. Baseball is a game," he said.
"You look at the real-life perspective when things go on. That's the last thing I want to do or any team wants to do, especially when something is going on five minutes down the road.
"You've got to tell your families how much you love them. They come to work and a tragedy like this happens. It's hard to put into words. You just kind of got to go about your day and have their thoughts and prayers in your mind."