The d-man was injured during the first period of Thursday's game against Tampa Bay where he got caught up behind the Ottawa goal with Ondrej Palat.
"He's going to miss some time," Sens head coach D.J. Smith said Saturday from Philadelphia. "We don't know the exact timeline but it'll be somewhere around that four week range."
Zaitsev has one goal and one assist in 22 games this year. The Russian averages 18:32 a game, with 2:23 coming on the penalty kill.
"It hurts us defensively," Smith said. "I think he was playing probably as good as he's played. He and Thomas Chabot were really meshing together there.
"'Z' is one of the more underrated players we have. You're losing an elite defender and a really good penalty killer."
