The former Huddersfield second rower hurt his left knee during Sunday's 18-16 home defeat by his old club.
"Danny is having an operation on a cartilage today," Wildcats coach Richard Agar said. "It's going to rule him out for three to four weeks. It's a big blow because he's become a very important player for us and we've not got the biggest squad."
"He's got that line-breaking ability and he's really grown into the captaincy."
Agar will plug the gap for Saturday's game against Catalan Dragons in Perpignan by bringing in either Frankie Mariano or Kyle Trout, who has been recalled from his spell at Doncaster.
Former Hull KR forward Mariano would have been the automatic choice but he has not had any game time for a fortnight.
Agar wanted him to play alongside Trout on a dual registration for Doncaster but the Championship club's coach Tony Miller was unable to find a place in his team.
Agar has no argument with Miller but he believes the case highlights the drawback of the controversial dual-registration system - which several leading Championship clubs are fighting, claiming it undermines the integrity of their own competition.
"We had to leave Frank out of the team because we felt some other guys deserved a chance but we haven't seen him play since," Agar said. "The dual reg hasn't quite worked for us. We'd have obviously preferred him to go to Doncaster and get a couple of weeks in but they've had no spot for him.
"I appreciate where the Championship clubs are coming from. They want their own identity and they don't want blokes in for a week and out for a week. Nor would I expect them to pander to us. Tony is trying to build his own team and culture so I guess it's disruptive having blokes in and out."