The two men, the skipper and first mate, were placed under pre-trial detention after giving testimony that began early Wednesday and concluded in the early hours of Thursday, the state news agency ANA said.
Eleven other crew members were conditionally freed.
The fire last Friday drew fury after Hydra's firefighting team said it was sparked "by a fireworks launched from a boat" and ravaged the island's sole pine forest.
There was further anger after it emerged that a group of wealthy Kazakh nationals who had chartered the superyacht were allowed to leave Greece without testifying.
Hydra mayor Giorgos Koukoudakis told public television channel ERT that he was "outraged that certain people are starting fires in such an irresponsible manner".
The news also sparked fury on social media.
Greece has recently toughened penalties for arson, with perpetrators now facing up to 20 years in prison and a fine of up to 200,000 euros.
Authorities have warned that strong winds and high temperatures spelt a very high risk of forest fires.
Greece recorded its first heatwave of the year last week with temperatures of over 44 degrees Celsius (111 degrees Fahrenheit) in some locations.
Last year, a fierce two-week heatwave was followed by devastating wildfires in which 20 people died.
Scientists warn that fossil fuel emissions are worsening the length and intensity of heatwaves around the world.
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Forest and Wild Fires - News, Science and Technology
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