Kostelic was injured during the initial portion of the slalom leg and Pavlek said there was a potential for surgery.
A team statement late Sunday said that an initial MRI in Krasnaya "detected no vital new damage," adding that the pain could be from "heavy knee joint stress.
"But tomorrow Ivica will head toward Basel, Switzerland, where a second MRI will be done," the statement added. "And tomorrow in (the) afternoon hours new decisions considering therapy will be made."
It was Kostelic's sixth win this season and the 24th of his career. He also now has five crystal globes for World Cup titles - one large one from last season's overall victory and four smaller ones for discipline titles, two in super-combi and two in slalom.
Beat Feuz of Switzerland dropped from first after the downhill leg to finish second, 1.16 seconds behind, and Thomas Mermillod Blondin of France was third, 1.77 back.
Feuz won the downhill Saturday and would have won the super-combined title if he had also won this race. Now, depending on Kostelic's status, Feuz could be poised to win the overall World Cup title.
With six more stops on the circuit this season, Kostelic holds a 70-point lead over Feuz in the overall standings, with Austria's Marcel Hirscher third, 218 points back.
Kostelic won the super-combi title with 336 points, 36 ahead of Feuz.
"I'm very sorry for Ivica," Feuz said. "I really hope it's not so bad and that he's able to join us again soon. He's a great champion and I hope he's not in too much pain."
In his downhill run, Feuz soared into the air for about 80 yards off the Rosa Khutor slope's biggest jump, landing outside the blue paint that outlines the course.
"The downhill was good but the slalom was really difficult for me, but I've got another podium finish and I couldn't dream for a better season," said Feuz, who held all of his fingers out wide during the post-race celebration to celebrate his 10th podium finish of the season.
It was the second podium of Mermillod Blondin's career, having also finished third in a super-combi in Bansko, Bulgaria, last season.
"It's a very good thing to be on the podium here two years before the Olympic Games on the same slope," the Frenchman said.
All of the Americans entered went out in the slalom run. Bode Miller sat fourth after the downhill portion but failed to make a gate on the top, while Ted Ligety and Will Brandenburg straddled on the bottom.
The downhill and slalom courses are next to each other, and share the same finish area.
Both runs were held in flat light with only a few hundred fans on hand, due to heavy security.
The men's circuit now moves to Bansko, Bulgaria, although the top men will be back in Russia for a special parallel race in Moscow on Feb. 21. The women's circuit arrives and begins downhill training here Wednesday.
Feuz is planning to skip the technical races in Bansko before returning to the circuit in Moscow.