Coindesk reported on Thursday that the loss is about 4,736.42 Bitcoins, worth more than $60 million.
"Are we going to get our btc? or might as well just forget it. Your press release said nothing about sending us what you owe. I have 4000$ stuck in your wallet which is now almost 4300$," tweeted a user named Lohit.
Another NiceHash user Philip Richardson tweeted: "If I dont get my BTC back i will never use your service again".
Earlier in the day, the value of one Bitcoin had crossed $14,000, a new record high for the cryptocurrency.
Bitcoins are created through a complex computer process known as mining and then monitored by a network of computers across the world.
A steady stream of about 3,600 new bitcoins are created a day - with about 16.5 million now in circulation from a maximum limit of 21 million, BBC reported.
"Clearly, this is a matter of deep concern and we are working hard to rectify the matter in the coming days. In addition to undertaking our own investigation, the incident has been reported to the relevant authorities and law enforcement and we are co-operating with them as a matter of urgency," NiceHash said.
The company recommends users to change their passwords - both on NiceHash and other services.
The incident brings back the memories of the 2014 implosion of the "mtGox" Bitcoin marketplace which lead to losses of millions of dollars.
In India, the Reserve Bank of India (RBI) this week cautioned the "users, holders and traders" of Bitcoins about the security-related risks associated with dealing with such virtual currencies (VCs).
The apex bank reiterated its stand that "it has not given any license or authorisation to any entity or company to operate such schemes or deal with Bitcoin or any VC".
"In the wake of a significant spurt in the valuation of many VCs and rapid growth in Initial Coin Offerings (ICOs), RBI reiterates the concerns," the central bank said in a statement.
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