Costigan, a Queensland State of Origin back rower, re-injured his quad during the Raiders round one loss to Newcastle.
He is joined in the casualty ward by Glen Turner who is out for the next four to six weeks with an ankle injury.
Raiders coach Neil Henry has added Nigel Plum and Joe Picker to his squad for Saturday's clash with Penrith at CUA Stadium, with Marshall Chalk elevated to the starting line up for Turner and Trevor Thurling named as 18th man.
Henry said although the loss of Turner and Costigan was significant, he was confident both Plum and Picker would fit nicely into the squad.
"We have some depth in the back row and Marshall Chalk was pretty good when he was there last week, and Nigel Plum comes back from a shoulder reconstruction so he's fit and raring to go," Henry said.
"Joe Picker is also in the background ready to go from the bench. We have a little bit of depth, which you would hope at the start of the year, and hopefully we don't get any more injuries."
Hooker Lincoln Withers (ribs) and fullback William Zillman (concussion) will need to pass fitness tests prior to the Panthers clash, while prop Scott Logan has been cleared of any serious knee damage and will play.
Withers was confident of being fit for the match.
"It's a bit painful still but I'll train this week and consult the medical staff and go from there," Withers said.
"It's one of those injuries where you have to put up with the pain factor and I'll have to check it out with the doctor and then talk to Neil."