The Packers were 6.5-point favorites over the Saints last week in an early line available at the Westgate SuperBook in Las Vegas. When the Westgate reposted the line Sunday night, after Rodgers' injury, New Orleans was a 3.5-point favorite.
Rodgers suffered the injury in the first quarter of the Packers' 23-10 loss to the Minnesota Vikings on Sunday. The team said he could miss the rest of the season.
Rodgers missed seven games in 2013, after breaking his left collarbone. The injury to his right (throwing) shoulder is expected to keep him out longer.
Heading into the weekend, the Packers were the favorites to win the NFC at the Westgate and were behind only the New England Patriots in the book's odds to win the Super Bowl at 5-1.
Westgate head football oddsmaker Ed Salmons said he was waiting for an official timetable on Rodgers, but went ahead and moved the Packers' Super Bowl odds to 12-1 after the injury.
"If they say he's done for the year, they're going to go a lot higher," Salmons said.
If Rodgers is ruled out for the season, Las Vegas sportsbook operator CG Technology said it would likely move the Packers to around 30-1.
Brett Hundley, a third-year pro out of UCLA, replaced Rodgers against the Vikings and is expected to be the starter against the Saints. Hundley completed 18 of 33 passes for 157 yards with a touchdown and three interceptions against the Vikings.
CG Technology vice president of risk Jason Simbal said, in his opinion, Rodgers is the most valuable player to the line in the NFL, even more than New England Patriots quarterback Tom Brady.
"It's more about the quality of backups than the difference between Rodgers and Brady," Simbal said.
The Packers had attracted the second-most bets to win the Super Bowl at CG Technology, behind only the Patriots.