The three Greeks, aged between 21 and 31, were arrested on the island of Samos with the assistance of a Latvian helicopter from EU border agency Frontex.
The three suspects were dressed like Greek coastguards and wore hoods.
One of them was spotted on Thursday aboard a boat carrying migrants to the island.
As soon as the migrants had landed onshore, the suspect made off with the boat engine, the coastguard said.
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A search of the suspects' homes and storage areas belonging to relatives turned up the sum of 15,000 euros (USD 17,000) in various currencies, five boat engines and a box containing wet, mostly children's clothes.
Activists have received numerous reports of raids on migrants in the eastern Aegean Sea.
In past weeks, victims said they had been confronted by men dressed like "commandos", who ripped their clothes and underwear in search of cash, and made off with their boat engines.
Nawal Soufi, an Italian activist who has handled numerous distress calls from Syrian refugees at sea, said she had heard of around 20 boats whose passengers had been attacked in recent months.