Gordon played 11 minutes before reinjuring the finger, collecting seven points, two assists and two blocked shots.
Gordon recently missed 16 games after undergoing surgery to repair a fracture to the same finger. He has played in the Pelicans' past four games, averaging 22.7 points in the first three games and scoring seven points in 11 minutes before ending his night early against Utah.
"I don't know for sure what happened, but it looks like he might have done the same thing again," Pelicans coach Alvin Gentry said. "And that would be unfortunate because he worked so hard to get back. I thought he was really playing really good basketball. For that to happen to him again, if it's gonna be six to eight weeks -- and I'm just speculating right now, I don't know that for sure - but if that's gonna be the case, it pretty much takes him until the end of the season."
Jrue Holiday started the second half in place of Gordon, and Gentry said after the game that he may look to start games with Holiday in Gordon's absence.
"At some stage, we have to start thinking about the future, looking at the future," Gentry said. "That's one of the reasons why I stuck Jrue out there to start the second half. We have to start looking at Jrue as a starter some and playing him."
Gentry expanded on how to evaluate the team for the future, noting New Orleans' long odds of making the playoffs.
"At this stage, like I said, it would be a miracle almost for us to make the playoffs. We really have to start looking at developing a culture and how we're gonna play in the future and figuring out guys on this team, how they fit into the system and if they're going to be able to fit in a system."
Set to be an unrestricted free agent for the first time in his career this summer, Gordon is averaging 15.4 points, 2.7 assists and 2.3 rebounds in 45 appearances. The 27-year-old has yet to play more than 64 games in a regular season in his five years with New Orleans.
Tyreke Evans (right knee), Quincy Pondexter (left knee) and Bryce Dejean-Jones (right wrist) have already been ruled out for the rest of the season, and Alexis Ajinca missed his second straight game with a fractured sternum.
Pelicans players have combined to miss 183 games this season, according to data provided by Jeff Stotts of InStreetClothes.com, putting them in the top five in the league in that category in two of the past three seasons.
New Orleans has also used 28 different starting lineups this season, tied with the Philadelphia 76ers for most in the league.