The auxiliary officers were responding to a call-out early on Monday morning and had stopped at a traffic light at a road junction when they noticed the car stationary in the middle of the two lanes.
The driver jumped out and shouted to them that his wife had gone into labour.
The officers ran to help and were just in the nick of time: the baby's head was already visible.
The next minute the baby “slipped out” completely, according to a police news release.
Luckily one of the policewomen was able to catch the baby girl who soon began to exercise her lungs.
The second officer wrapped the baby in her pullover and got into the car next to the mother while her colleague tried to calm down the woman's husband.
Help arrived soon afterwards and the baby and her parents were soon transported to hospital, where the little girl was said to be doing well.
One of the two officers, 55-year-old Sandra Häusermann, told the Blick newspaper it was the nicest thing she had experienced in 33 years in the force.
“I can't find words for my feelings,” she was quoted as saying.