Police declined to provide further details about the insult when contacted by Reuters, saying an investigation had been launched.
Merkel's popularity has waned due to her liberal migrant policy. More than a million migrants arrived in Germany last year, many of them fleeing war and poverty in the Middle East and Africa, and concerns about how Europe's largest economy will be able to integrate them are now rife.
An INSA poll published on Wednesday showed that almost half of Germans did not want her to stay in office for a fourth term after an election next year.