Officers received a call for help and arrived to see the animal still chasing the caller in Karlsruhe, Germany.
Police said on Twitter the man told them: “Help, I’m being pursued by a squirrel.”
Officers launched their own chase for the squirrel which they caught and the animal fell asleep.
Police say the rodent has now become their new mascot and has been dubbed Karl-Friedrich.
The animal is being well looked after in an animal rescue centre.
Karlsruhe police posted a tweet about the case on Thursday with more pictures of the squirrel in custody.
A police spokeswoman said squirrels that have lost their mothers often focus on a person as a replacement.
She said it can be “pretty scary” and added that the caller “was certainly feeling a bit threatened”.
Squirrel attacks can sometime be serious – in July 2017 New York authorities put out warnings about an unusually aggressive squirrel in Prospect Park which had attacked five people in one week.
In Cornwall in the UK a three-year-old boy was bitten by a pack of six squirrels in 2016.