The Chinatown star took a tumble outside a fitness centre in Los Angeles, cracking a bone in her arm and cutting her head.
Surgeons fitted a metal plate into her wrist, but she has suffered complications and now wants to delay a court case.
Her former employee, John Paul Horstmann, is taking action against Dunaway over allegations she owes him $5,780 (£3,853) for three weeks work for which he was never paid, according to TMZ.com.
Dunaway has reportedly written to the judge overseeing the case asking for more time to prepare while she recovers from her injuries. The case is due back in court next month (Jan11).