In 2013/14, York Theatre Royal and Sheffield Theatres reported the number of BME employees as 3%, while Hull Truck Theatre had none.
ACE said that a survey showed that 14% of the English workforce were from BME communities.
Hull Truck Theatre said it was taking action to address the issue.
Last year Sir Peter Bazalgette, chair of Ace, said organisations could have their funding cut if they failed to improve diversity.
Speaking at the launch of the new report, Sir Peter said theatres had to make "their work more reflective of their communities, and representative of 21st Century England".
"The arts can show us how things are and the arts can give us a vision of what they could be," he said. "They can make the case for diversity; they can be the case for diversity. They can bring us together."
Ace said it was providing Â£8.5m of funding to encourage diversity.
The executive director of Hull Truck Theatre, Janthi Mills-Ward, said the theatre had introduced an apprenticeship scheme "which has changed the demographic".
"Hull's demographic is actually 94% white," she said. "So actually, young people, or anybody from Hull from a BME community might not have seen a career in the arts as something they could go in to."
A number of theatres in Yorkshire employ fewer than 5% black or minority ethnic (BME) workers, according to an Arts Council England (Ace) report.