The pursuit started just before 8 p.m. and ended at Vermont Avenue and Martin Luther King Jr. Boulevard, Los Angeles Police Department said.
The officers were chasing a driver they suspected might be under the influence when the crash happened.
The injured women were conscious and breathing following the crash and were transported to the hospital.
It was not clear whether the officer or officers in the police vehicle were injured was not available.
Police did not say whether the women were the suspects being pursued or bystanders.
City News Service contributed to this report.