Tanev sustained a dislocated shoulder during Game 6 of the Western Conference quarterfinals against the Dallas Stars and will have surgery next month.
The 32-year-old veteran blueliner is expected to be sidelined for four to six months.
Tanev told reporters the extent of the injury during his end-of-season media availability after the Oilers eliminated the Flames in Game 5 Thursday.
"We'll see how it goes," Tanev said Saturday. "After the surgery, I'm sure that our medical staff will have more of an update on how it went and more of an exact time frame maybe, I don't know. Four to six months is kinda big but that's what I've been told."
Tanev had six goals and 28 points during the regular season plus one assist in eight playoff games.