The Eagle S, a Cook Islands-registered tanker, is accused of dragging its anchor across the seabed, damaging five undersea cables on Christmas Day.
The captain (a Georgian national) and the two first officers (Indian nationals) are facing charges of aggravated criminal mischief and aggravated interference with communications.
The incident disrupted electricity transmission between Finland and Estonia and also damaged telecommunication cables.
The Eagle S is believed to be part of a "shadow fleet" of tankers used to transport Russian oil in violation of sanctions.
The defendants are contesting Finland's jurisdiction in the case, arguing that the damage occurred outside Finnish territorial waters.
The damage to the Estlink 2 cable, which provides a significant portion of Estonia's winter electricity, did not cause a service disruption but did increase energy prices in the Baltic region.
While the incident is being treated as a criminal act, some intelligence agencies speculate that it may have been accidental, due to the ship's age, poor maintenance, and inadequate crew training.