Ablett, a second rower who proved an effective stop-gap centre this season, sustained a hand injury in the Rhinos' 24-8 Tetley's Challenge Cup defeat at Huddersfield last Saturday while Peacock has injured his knee.
Leeds are also likely be without forward Brett Delaney for the visit of St Helens next Monday after he picked up a shoulder injury at the John Smith's Stadium.
"It is a blow to lose both Carl and Jamie, especially considering the form that both players are in at present," said Leeds coach Brian McDermott.
"The worst case scenario is that both are out for eight weeks but our medical staff will be working hard with them.
"Brett Delaney is also struggling with the shoulder injury he suffered against the Giants and he may miss out this week.
"It is obviously a blow to lose two internationals from our squad for two months but injuries are something that is part of our game and that is why you have a squad to draw upon.
"Stevie Ward is also out and Ben Jones-Bishop is a couple of weeks away from making his return but this will give an opportunity to other players to stake their claim in the team over the next few weeks."
- Sports & Recreation
- Brett Delaney