The interior ministry said in a statement that the district chief for Monastir in central Tunisia and three policemen from Marsa, a northern suburb of Tunis, were sacked for "abuse of power".
Ministry spokesman Mohamed Ali Aroui said their sacking was linked to "cases of coffee shops that stayed open during the time of fasting".
He declined to give further details.
During the holy month of Ramadan, which started last week, believers must abstain from eating, drinking, smoking and having sex from dawn to dusk.
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"He also grabbed a chair and chased a waitress who ran outside the shop and struck her with it," said Fares, adding that he had lodged a complaint against the officer.
A video posted online shows several people running out of a cafe in panic and a man in a suit running after a young woman in the street. He is seen shoving her, grabbing her cell phone and hitting her.
There is no law in Tunisia that prohibits people from eating or drinking in public during Ramadan.
Aroui told AFP, however, that "for decades" coffee shops in tourist areas and malls have been allowed to remain open throughout the day in Ramadan.