He broke his hand in a scrimmage at training camp Sunday, and Tuesday's surgery was to stabilize the fracture.
The Capitals acquired Edmundson in a trade with the Montreal Canadiens on July 1.
"It's not ideal, definitely, team-wise and for him individually, personally," Capitals coach Spencer Carbery said of the injury. "Just the timing of it, new organization and right away just (getting injured). But on the bright side, it's an opportunity for some young guys and it could have been worse."
"I felt like he was in a really good place, getting here a little bit early, starting to integrate himself with the group," Carbery added.
The Capitals sent third- and seventh-round draft picks in 2024 to Montreal for Edmundson, who will become a free agent after the season.
Edmundson, 30, had two goals and 11 assists in 61 games for the Canadiens in 2022-23. The 6-foot-5 Manitoba native ranked second among Montreal defensemen in hits (112) and blocked shots (149).
He won a Stanley Cup with St. Louis in 2019 and has 104 points (28 goals, 76 assists) and 438 penalty minutes in 477 games with the Blues (2015-19), Carolina Hurricanes (2019-20) and Canadiens.
The Capitals open the season Oct. 13 against the visiting Pittsburgh Penguins.