Leeds-based Northern Ballet said it was asking for sponsorship because 10 out of 40 dancers faced redundancy if it failed to plug an Â£800,000 shortfall.
The Arts Council announced in March it would cut its grant to the company by 25% in 2012-13.
Northern Ballet said maintaining a full complement of dancers was "vital".
Mark Skipper, the company's chief executive, said: "We can't expect our dancers to deliver 150 performances in 24 cities across the whole of the UK without resources.
"It's a very limited profession and to lose 25% of the workforce of classical dancers in the north is appalling."
Mr Skipper said attracting sponsorship for dancers was just one of "several" initiatives the company was considering to fill the black hole left by the Arts Council funding cut.
Earlier this year, Northern Ballet's production of Cleopatra, the story of the Egyptian queen and her lovers, brought in about Â£1.2m at box offices across the UK.
But Hannah Bateman, first soloist at Northern Ballet, said the company could only continue its success if it remained at full strength.
"I really don't know what will happen if we do lose dancers. We're on a skeleton staff of dancers as it is," she said.
A Yorkshire ballet company facing the loss of a quarter of its dancers due to funding cuts is appealing for people to sponsor a dancer in a bid to save jobs.