"An investigation has been ordered in relation to pictures posted on websites and social media, showing punishable acts by a police officer," the department said in a statement.
A video frame grab posted by Greek media show the officer, who is holding a knife, slap the migrant outside the Kos police station.
Scores of migrants are standing outside the station, waiting to be documented so that they can sail on to Athens.
Greece has been overwhelmed by an influx of migrants and refugees mainly from war-torn Syria this year.
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The UN refugee agency's division for Europe said 124,000 refugees and migrants have landed in Greece since the beginning of the year.
The agency said that Athens' response to the problem had so far been "totally shameful", with many of those landing on the eastern Aegean islands near Turkey usually forced to sleep in the open, lacking access to washing facilities and toilets.
Greek authorities are currently completing a container park near central Athens to relocate hundreds of migrants currently sleeping in one of the capital's parks.