Seven people took part in the lawsuit filed at the Tokyo District Court, plaintiffs' lawyer Hiromu Mochizuki told AFP before the filing.
The hack of Coincheck -- resulting in the disappearance of NEM cryptocurrency worth $530 million (roughly Rs. 3,400 crores) -- was one of the largest of its kind, and prompted authorities to search the firm's office earlier this month, after slapping it with an administrative order.
The company has pledged to reimburse about $400 million (roughly Rs. 2,460 crores) to all 260,000 customers who lost their holdings of NEM, the 10th biggest cryptocurrency by market capitalisation.
Coincheck halted operations after the hack and prevented traders from withdrawing their virtual currency from the exchange -- a decision that left those assets in limbo while the cryptocurrency markets continued to move.
"Plaintiffs are demanding Coincheck return their cryptocurrencies -- 13 different kinds including NEM," Mochizuki said.
On Tuesday, Coincheck said it had resumed operations for withdrawals denominated in Japanese yen but has still frozen withdrawals of a dozen different kinds of cryptocurrencies.
Plaintiffs are demanding the reimbursement of their digital cash and also considering calling for compensation for the drop in their assets' value while withdrawals were halted.
Japanese officials have suggested Coincheck lacked proper security measures, leaving itself vulnerable to theft.
In the wake of the theft, the country's Financial Services Agency instructed more than a dozen local exchanges to submit reports on their efforts to monitor systemic risks.
Thieves syphoned away 523 million units of the cryptocurrency NEM from Coincheck during the January 26 hack, exceeding the $480 million in virtual currency stolen in 2014 from another Japanese exchange, MtGox.
That hack prompted Japan to issue new regulations, requiring exchanges to obtain a licence from the FSA, but Coincheck was allowed to continue operating while the agency was reviewing its application.