The defender was forced off during last weekend’s match against Manchester City, and David Moyes confirmed he will miss the rest of the season.
The former Manchester United handler will now decide whether to start Jake O'Brien or Michael Keane against the Blues at Stamford Bridge.
Moyes told the media: "Tarky's out, he's going to be out for the rest of the season. He'll have an operation on his hamstring.
“It's a big blow for us because Tarky has played such a huge part of what we've done and how we've done so well in this period. I think he'll be back for pre-season but it could eat into that.
"Jake is a centre-half so I'm not worried about doing it, that's for sure. It's just trying to get the right balance for the team.
“He's done a brilliant job at full-back so it 's just weighing up whether we want to make one or two changes in position.
“We've got Michael Keane so we have options and we'll look to play those options to see what works best.”