Corbin said Millsap "fell funny" during the second half against the Rockets and played through the sprain. Adrenaline wore off and pain kicked in postgame, though, forcing the Jazz to seek outside assistance.
"He's not one to look for a way out. He must be really hurt. So we just hope it's something temporary," Corbin said.
The injury initially appears to be not serious, which is positive news for a Utah team fighting for a playoff spot with just seven games to go.
Depending on Millsap's progress, the Jazz could be down to nine active players Friday at New Orleans.
Reserve forward Jeremy Evans (sprained right ankle) is doubtful for the final two games of Utah's road trip. Josh Howard, Raja Bell, C.J. Miles and Earl Watson are already out with injuries.
Corbin considered inserting newly signed point guard Blake Ahearn against the Rockets, nearly pulling the trigger at the start of the fourth quarter.
Corbin held off, starting point guard Devin Harris picked up his fifth foul with 11:51 to go, and Utah's coach immediately wanted to kick himself.
Veteran Jamaal Tinsley guided the Jazz down the stretch, though, and Corbin acknowledged Thursday that Ahearn ideally will see action only in a winning situation.
"It's really not fair to him to throw him out there when he [doesn't] know and the game's tight and guys are pressuring him and he has to try to think his way through plays," Corbin said.
Even before Millsap's injury, Corbin was left with few options in selecting Utah's starting lineup.
Devin Harris, Gordon Hayward and Al Jefferson are locked in, while DeMarre Carroll has recently filled in for Miles.
Corbin could start rookie Alec Burks at shooting guard and move Hayward back to small forward. Carroll has played well in two of the Jazz's past three games, though, while Hayward excelled Wednesday as Utah's primary shooter.
With the remainder of the Jazz's roster either injured or inexperienced, Corbin said his hands are tied as Utah eyes the postseason. And he laughed Thursday when asked if Carroll's starting either because A) Corbin doesn't have another choice or B) Carroll's the right guy for the job.
"A's right," Corbin said.
Jazz at Hornets
P At New Orleans Arena
Tipoff • 6 p.m., Friday
TV • ROOT Sports
Radio • 1320 AM, 1600 AM, 98.7 FM
Records • Jazz 31-28, Hornets 16-42
Last meeting • Hornets, 86-80 (Feb. 13)
About the Jazz • They have won three of four games, with victories against Houston and San Antonio. … Utah's Feb. 13 loss to New Orleans came against a short-handed Hornets team and followed an important road win against Memphis.
About the Hornets • They've won two of three and are in the middle of a five-game homestand. … Eric Gordon, Trevor Ariza and Emeka Okafor didn't play Wednesday in a win against Sacramento due to injuries. Jarrett Jack is out for the season.