The four, all Syrian nationals aged between 30 and 41, are accused of "causing the death of more than one person" and "trafficking migrants", the Dogan news agency reported.
They are to appear in court later today and television pictures showed the men being led away by police as they covered their faces.
Twelve migrants drowned on Wednesday when two boats sank in Turkish waters, in the latest tragedy to hit people seeking to cross the Aegean to Greece.
His four-year-old brother, Ghaleb, and their mother, Rihana also drowned when their boat sank.
Reports have said that the family, from the Syrian mainly Kurdish town of Kobane, wanted to eventually reach Canada.
There has over the last weeks been a dramatic spike in the numbers of migrants -- mainly from Syria, Afghanistan, Pakistan and Africa -- seeking to leave Turkey by sea for Greece in the hope of finding new lives in the European Union.