Bird died in her sleep, and though the cause of death wasn't reported, she had an operation to remove a tumor in April related to anaplastic thyroid cancer, her partner, whose name wasn't reported, said in a statement.
"Despite a determined fight, she had come to terms with the inevitable in the last few weeks and died peacefully in her sleep," the statement said.
Carlyle paid tribute to Bird on Twitter, Britain's The Guardian reported.
"Such a said day today. RIP Antonia Bird. Farewell my beautiful friend," he wrote.
Bird directed Carlyle in 1994's "Priest," 1997's "Face" and 1999's "Ravenous," the BBC reported.
In a 1999 interview with The Guardian, Bird said she preferred to work with British actors because they "arrive on the set and they have an idea of what they want to do in the scene."
"They've thought about it, they come and offer you something as a director," she added. By contest, U.S. actors "arrive on set a blank book."
"Now that's fine, that's their tradition, but as a British director it's absolutely terrifying," she said.