The Cardinals said they learned about the positive tests late Thursday night and have instructed all players and staff to self-isolate in their hotel rooms in Milwaukee until further notice. The team also said nobody left for Miller Park on Friday morning.
MLB's quick decision to postpone Friday's game, which was scheduled for 2:10 p.m. ET, comes after the outbreak within the Miami Marlins, who have had 21 positive tests -- 18 by players over the past week after another on Friday.
The postponed game has been rescheduled as part of a doubleheader on Sunday, with the first game to start at 2:10 p.m. ET. The league and the MLB Players Association announced Friday that doubleheaders will now be seven innings in length for each game.
Saturday's game remains scheduled for 7:10 p.m. ET.
MLB said Friday's postponement allows enough time for the Cardinals to do additional testing and conduct contact tracing. A source told ESPN's Jesse Rogers that if what is happening with the Cardinals had occurred before the Marlins' outbreak, Friday's game at Miller Park would still be played.
"We are supportive of Major League Baseball's decision to postpone today's game and look forward to playing our home opener as soon as conditions safely allow," Brewers president/general manager David Stearns said in a statement. "The health and safety of our players and employees are, and will continue to be, our top priorities."
The two Cardinals players that tested positive were among the 29 around Major League Baseball -- 20 players and nine staff members -- to be infected out of the 11,895 samples collected over the past week through Thursday, the MLB and MLBPA announced Friday.
The Cardinals played in Minnesota on Tuesday and Wednesday before a scheduled day off Thursday. The Twins hosted Cleveland on Thursday night, meaning the Indians likely used the same visiting clubhouse as St. Louis. Minnesota is scheduled to host Cleveland again Friday night.
This brings the number of teams being held out of action on Friday to six. The Brewers and Cardinals will join the Marlins, Philadelphia Phillies, Washington Nationals and Toronto Blue Jays as teams affected by the fallout from positive tests.
Brewers principal owner Mark Attanasio shrugged off the setbacks and said baseball is braced for curveballs, especially this year.
"We're all committed, I believe -- and I've talked to a number of players today -- to finishing the season," Attanasio said. "Insofar as we can continue to provide some enjoyment for our fans, I think that's something we're all committed to doing. ... If we're not smart and safe, then we'll fail. But we're doing everything we can not to fail."
The Cardinals' positives represent the first positive tests the sport has seen outside of the East Coast since the regular season started last week, leaving concern that the season might be in jeopardy.
"That's a concern of mine,'' said Colorado Rockies outfielder Charlie Blackmon, who was out with the virus earlier. "I speak for the entire Rockies team -- we want to go out and play. ... Anything that pops up negatively, in terms of this virus situation, could hinder that. So yeah, I'm concerned. I would rather not see any more positive cases.''
The Associated Press contributed to this report.