The 32-year-old former New Zealand international, who missed the last three months of his final season with Leeds due to a knee injury, played in the Dragons' opening three matches of Super League XVIII.
But he picked up a back injury in his side's 26-14 defeat at Warrington last month, a match in which he was sent off and subsequently suspended for one game, and has failed to overcome the injury with rest.
Webb will undergo surgery on Friday and the club say he will be sidelined for between four and six months.
It is the second major blow to the Catalans, who are still without Australian scrum-half Scott Dureau after he underwent surgery in December to remove a brain tumour.
Dureau, who has made the Super League Dream Team in each of his first two seasons in Perpignan, was recently given the all-clear to resume training but he is not expected back playing for several more weeks.
"It's obviously really bad news, especially after Scott Dureau's surgery," said Catalan coach Laurent Frayssinous.
"They are two key players in the squad and two of the best players at their position in Super League. The team had to face a couple of pieces of bad news since November and has always found the strength to overcome that.
"The Brent Webb long-term absence is an opportunity for other players who deserved it to play in Super League and earn their place on the team sheet."
Webb, who made 155 appearances for Leeds after joining them from New Zealand Warriors in 2007, signed a two-year contract with the Dragons.