The team said Freeman will wear a cast for four weeks. He is expected to miss 10 weeks, according to the team.
President of baseball operations John Hart said he knows no player can replace the production lost by the injury to Freeman, who shared the major league lead with 14 homers and was hitting .341.
Hart said Freeman's injury was especially tough "with the historic year he was putting together."
Freeman leads the majors with a .748 slugging percentage and is second with a .461 on-base percentage. His 2.5 WAR was tied for third in the majors. He also ranks among the NL's top three in runs and extra-base hits.
"The more disappointing fact is we had started playing good baseball as a team," Freeman said. "I never play this game for myself. I just come in every day to try to help this team win and get back to the playoffs because it has been four years. ... I could care less about personal statistics at this point."
Braves general manager John Coppolella said he "will leave no stone unturned" in his search for help at first base through a trade. He said veteran first baseman Ryan Howard, who was released from Triple-A Gwinnett on May 8, is not an option.
The team also is closing in on a minor league deal with free-agent first baseman James Loney, sources told ESPN's Buster Olney. Loney was with the Rangers in spring training and played in the minors with the Tigers this season.
"We couldn't find anybody that could do what Freddie does," Coppolella said. "He was arguably the best player in the whole league."
"He's irreplaceable," Peterson said of Freeman. "I'm not going out there to do what Freddie Freeman does. I don't think that's possible."
Atlanta was already thin in the infield after placing third baseman Adonis Garcia on the disabled list with Achilles tendinitis before Wednesday's game.
The Braves recalled infielder Rio Ruiz from Triple-A Gwinnett in a corresponding move. Ruiz is starting at third base Thursday night and batting eighth.
Ruiz, 22, played in five games with Atlanta last season. He was hitting .262 with 4 home runs and 16 RBIs in 37 games with Gwinnett.
Ruiz and utility infielder Johan Camargo were working at first base before batting practice on Thursday.
"Obviously, this is quite disappointing," Freeman said, wearing a green cast on his left wrist. "Obviously it's a tough blow. I'm going to do everything I can to get back as soon as I can."
Freeman said he knows Loup had "no intent" to hit him with the pitch.
"He was just trying to get me out," Freeman said. "The best way to get me out is to throw inside. He just threw one that got away."
Freeman said he feared he suffered a fracture when first examined by trainer Jim Lovell on the field and Lovell "told me to squeeze his hand and obviously I couldn't do it."
No surgery will be required.
The umpires initially ruled that Loup's pitch did not hit Freeman. But with Freeman in obvious pain, the Braves challenged the call, and it was reversed after a video review.
The Associated Press contributed to this report.