Nine people including doctors, hospital staff and a translator were arrested on the island of Samos for allegedly furnishing asylum-seekers with false health certificates, enabling them to leave the island, state agency ANA said.
Thousands of migrants and refugees want to leave badly overcrowded camps on the Greek islands, but only minors, unaccompanied children and the sick are allowed to travel to other camps on the Greek mainland.
A day earlier, police said they had arrested six people on the island of Kos for allegedly helping migrants illegally fly to other European countries.
One of the suspects is a police officer who was working at Kos airport.
The gang would provide false travel documents to the migrants and receive between 4,500 and 6,000 euros per person, the police said.
Over the past week alone, over 40 migrants were arrested at island airports before flying to Belgium, Denmark, France, Germany, Italy, the Netherlands and Sweden on forged travel documents.
The new conservative junior minister for migration, Giorgos Koumoutsakos, this week said the government would speed up asylum background checks and pursue a "robust" programme of migrant returns to Turkey or their home nations.
Greece's previous leftist government had struggled to manage around 70,000 refugees and migrants, with around a fifth crammed into overcrowded facilities on Aegean islands facing Turkey, waiting for months for their asylum requests to be processed.