The dramatic incident happened in the heart of Glasgow near the Royal Infirmary on Monday evening.
Two men were reported to have attacked a white Mercedes A-Class that was stopped at traffic lights on Castle Street at its junction with Cathedral Square.
The suspects got out of a blue Seat Toledo taxi and attacked the windows of the Mercedes with knives. The 23-year-old female driver of the Mercedes managed to turn and drive back up Castle Street towards Alexandria Parade.
The two men are described as white men with a slim build. One was wearing a dark hooded top with the hood over his head and grey jogging bottoms. The second man was wearing a black tracksuit.
Detective Constable Kimberley Douglas said: "No one was injured in the attack but it was a frightening experience. Enquiries are ongoing to establish the full circumstances and CCTV footage is being reviewed.
"If you have any information about this incident or saw anyone matching the description of the suspects in that area around that time, please contact us on 101 quoting incident number 3911 of 16 September 2019 or Crimestoppers anonymously on 0800 555 111."