The group were caught on CCTV last Friday as they walked around the Renaissance Market Square. They then got into a horse drawn carriage.
Police spokesperson Sebastian Glen said officers were investigating the group’s “indecent antics”.
They could face up to 30 days in custody if convicted or a fine of 5,000 zlotys (£1,000) each.
Mr Glen said foreign tourists, notably those from Britain, who come for stag parties sometimes cause disturbance in the historic city.
Those who had been drinking alcohol were especially disruptive, he added.
In 2017, Baron Cohen, whose other characters include Ali G and Bruno, offered to pay the fines for six tourists arrested in Kazakhstan for wearing mankinis.
The Czech tourists had posed for photos in the country’s capital of Astana and were each given 22,500 tenge (£45) fines.
“To my Czech mates who were arrested. Send me your details and proof that it was you, and I’ll pay your fine,” Baron Cohen wrote on Facebook.
In 2012, the Cornish resort of Newquay banned mankinis in what came to be considered a successful attempt to reduce the crime rate.
Additional reporting by Associated Press
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