The woman was walking her dogs on Oxbarn Avenue in Merry Hill at around 8pm on Monday when it is alleged a man driving a black VW Polo mounted the kerb and drove at her in an attempt to run her over.
She moved out of the way but the driver wound his window down, spat towards her and then threatened her before driving off.
A 40-year-old man was arrested on Tuesday on suspicion of wounding with intent. He has been released on police bail while enquires continue.
Officers are appealing for any information.
Contact police via Live Chat or 101, quoting crime reference number 20WV/109550W/20.