A replacement for at least one of the women may be announced during Monday's season premiere, said executive producer Conrad Green.
"Obviously this has caught us a bit by surprise," he said, adding that any replacement would have "literally a couple of days to learn the routine, as opposed to a month."
"The show will go on," Green said. "But really, our thoughts are with Jewel and Nancy. It's such a tough blow for them and just horribly bad luck."
Jewel and O'Dell are the first contestants in eight seasons of "Dancing" to withdraw because of injuries sustained during pre-show training, Green said. Olympian Misty May dropped out last season after tearing her Achilles tendon during the competition.
Contestants could see their training time limited in future seasons, Green said.
"Usually the drama happens once the show has begun, not before the it starts," he said.
Jewel said in a telephone interview Thursday that she initially dismissed the pain in her legs as soreness from the show's six- to eight-hour daily rehearsals. She eventually sought treatment and was "completely shocked" by the diagnosis.
"The doctor just looked at me and said, 'You're done dancing,"' she said.
The 34-year-old singer-songwriter said she is in pain and using crutches and will have to be seated to perform her next two shows - scheduled for Thursday near Los Angeles and Saturday in Seattle.
"It's my first time sitting down in a concert," she said.
Jewel and O'Dell are still slated to appear on the show's season premiere Monday.
Jewel's husband, rodeo champ Ty Murray, remains a contestant on the program, though he said it's "a huge bummer" that his wife had to withdraw.
"That's a big part of the reason why we did the show," he said. "It was chance for us to work together and go through this together."
Jewel said she will continue to support her husband and her professional dance partner, Dmitry Chaplin, and she expects to return to the show.
"I think I'll be able to sing this season, so I can sing for Ty on the show if I can't dance for him," she said. "And I hope to dance with Dmitry again and vindicate ourselves."
Other contestants include Apple co-founder Steve Wozniak, rapper Lil Kim, former football star Lawrence Taylor, Olympic gymnast Shawn Johnson, singers Chuck Wicks and Belinda Carlisle, TV personality Steve-O, and actors David Alan Grier, Gilles Marini and Denise Richards.
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