The 37-year-old Russian tore the anterior cruciate ligament in his left knee during a 4-3 shootout loss to Tampa Bay on Thursday.
"He has a completely torn ACL and a deep bone bruise which has caused him a fair amount of pain," Senators general manager Bryan Murray said Saturday. "He will have surgery probably in two weeks.
"Certainly this year is over. The normal rehab they tell me is 3½ to four months minimum."
The 37-year-old has 18 goals and 31 assists in 77 games this season, and 990 points (412-578) in 1,228 career regular-season games. He has 98 points (44-54) in 116 playoff games.
The Senators will finish fifth in the NHL's Eastern Conference, and Murray said they will miss Kovalev's production in the postseason.
"Obviously in our top-six [forwards] all year," Murray said. "One of the guys we hoped and thought at playoff time would be a big factor for us.
"To lose him in the second-last game of the year, in a game that really didn't mean very much, is very disappointing for us as an organization and certainly for Alex."
Ottawa closes out its regular season Saturday night against the visiting Buffalo Sabres.