NHL Player Safety announced the punishment Wednesday.
Wilson made contact with Sundqvist's head while delivering a crushing hit as the Blues forward cut into the middle of the ice during the second period of Sunday's exhibition contest. He was given a 10-minute misconduct penalty and ejected from the game.
St. Louis head coach Mike Yeo, who said the center was "in a bad spot right now" because of injuries suffered on the play, took aim at Wilson's style of play, per Isabelle Khurshudyan of the Washington Post.
"It was predatory, and that is what he's done, and he's done that against us, so that's the way he plays the game," Yeo said. "We'll see what the league does."
Meanwhile, Caps general manager Brian MacLellan said Wilson must adjust his physical play in order to stay within the rules moving forward, according to the Washington Post's Barry Svrluga.
"He needs to be aware of how they're determining what's legal and what's illegal from the league's standpoint," MacLellan said.
Washington signed Wilson to a six-year, $31 million contract extension in July.
The 24-year-old Toronto native has 48 hours to appeal the decision. Dan Rosen of NHL.com provided further information about the process:
If Wilson accepts the 20-game ban, he'd be eligible to return Nov. 21 against the Chicago Blackhawks.