The team said it made the decision Tuesday after consulting with Major League Baseball as well as state and local officials. A makeup date was not announced.
The game had been scheduled for 7:05 p.m. at Camden Yards.
Riots broke out in Baltimore on Monday following the funeral of Freddie Gray, who died April 19 after suffering a severe spinal injury in police custody.
The Baltimore mayor's office said earlier Tuesday there were 144 vehicle fires, 15 structure fires and nearly 200 arrests in the unrest Monday. At least 20 officers were hurt, including six who were hospitalized and one in critical condition after a building fire, police said. Baltimore was under a 10 p.m. to 5 a.m. curfew beginning Tuesday, and all Baltimore public schools were closed as athletes with area ties, including Ray Lewis and Carmelo Anthony, pleaded for an end to the unrest.
The Orioles' home game against the White Sox also was postponed Monday night because of safety concerns, as rioters looted stores and threw rocks and bricks at Baltimore police about 3 miles from Camden Yards. The team announced the postponement about 40 minutes before game time. About 1,000 fans were inside the stadium at the time, and many gates already had been closed.
"I think I can speak for all of us: It's a little scary," White Sox outfielder Adam Eaton said Monday. "You never want anything to happen to anybody attending a baseball game, on the playing field or anybody in the city. We don't really want to tangle with that or put anybody in danger, so I think it's the best from everyone's perspective to cancel the game, and hopefully the police officers and officials can get the situation under control."
The Orioles and MLB are still discussing options for Wednesday's game against the White Sox and for weekend games with the Tampa Bay Rays, sources told ESPN's Jayson Stark. The White Sox were not scheduled to return to Baltimore this season.
Baseball commissioner Rob Manfred was in Baltimore on Monday for a trip that was planned long ago. He took part in the decision to postpone Monday's game.
"All I want to say about that is we are looking at every possible alternative in terms of completing the schedule in a timely way and making sure the games are played in a security situation that is safe for the fans," he said Monday night. "We are going to look at every alternative at this point."
That included the possibility of moving the series to Nationals Park in Washington.
Major League Baseball has postponed and shifted games in the past because of unrest.
In 1992, the Dodgers had four games postponed in Los Angeles after the Rodney King verdict.
In 1967, the Orioles and Tigers had a game postponed because of riots in Detroit. The next two games were shifted to Baltimore.
Information from ESPNChicago.com's Doug Padilla and The Associated Press was used in this report.