Computers were rendered unusable and business ground to a halt during the hack at the Townsend Business Centre earlier this month.
Locked screens displayed a sinister message demanding three 'bitcoins' in return for the safety of some files.
But the centre's CEO, Maragret McMahon, said they had a "lucky escape".
"We refused to pay the money, which we have been told would equal about Â£13,000 and reported the hack to the police," Ms McMahon said.
Bitcoin is a crypto-currency - a system of digitally created and traded tokens to which value is assigned.
Computers have to solve cryptographic problems in order to add blocks to the blockchain - a ledger that records every transaction that has ever occurred with Bitcoin.
In return, those computers receive bitcoins in a process known as bitcoin "mining".
Users have a "bitcoin address", to which bitcoins may be sent or from which they may be used.
Addresses are stored online in wallets that function like bank accounts.
Although most people refer to Bitcoin as a currency, it is worth noting that for regulatory reasons many countries - including the United States - have decided to define it as a commodity instead.
"Thankfully we were able to recover almost all of the information lost and our servers were restored within three days.
"The important thing to note is that we didn't have any specific vulnerabilities, but these criminals are incredibly intelligent.
"They could have been round the corner in Belfast or they could have been in Taiwan - we just don't know."
The business centre became aware of the hack on Wednesday 5th October and reported it to police who were able to advise what to do next.
David Crozier, from Queen's University's Centre for Secure Information Technologies, said these kinds of attacks are "increasingly common".
"Cyber criminals often demand to be paid in bitcoin as they believe it is an anonymous means by which they can be paid - but they are wrong," he said.
"Lots of people wouldn't think twice about buying physical security for their building such as alarms and heavy gates - but they are leaving themselves exposed to criminals online by not having the correct protection.
"We believe many of these crimes are going unreported and businesses are simply paying up - this is absolutely the wrong thing to do  because the hackers will keep coming back for more.
"Our advice is to act just as the Townsend centre did and make the PSNI aware."
The PSNI have said that an investigation is underway after the ransomware demand.
Det Chief Insp Dougie Grant, from the PSNI's Cyber Centre, said: "We have received a significant number of reports in relation to this type of cyber crime in recent months which is reflective of what is going on nationally and internationally and I would encourage anyone who is a victim to contact police as soon as possible."

Both Glasgow and Edinburgh said flights were back to schedule by 19:00.
A technical issue had caused delays to flights through all of Scotland's main airports.
Edinburgh, Glasgow, Aberdeen and Prestwick airports were affected by the incident at the Scottish Air Traffic Control centre at Prestwick.
Air traffic controllers Nats said there had been interference with some radio frequencies used to talk to aircraft.
The organisation has apologised to passengers and said it was also doing everything it could to safeguard the evening rush hour.
Nats said the faulty piece of equipment had now been removed from service.
All flights at Edinburgh Airport were delayed while three Glasgow Airport flights were cancelled  - one to Gatwick and two to Amsterdam -  and delays were expected throughout the day.
There were also a small number of delays on southbound flights from Aberdeen Airport.
Nats spokesman Paul Haskins told BBC Radio's Good Morning Scotland programme: "We've had a technical problem overnight with interference with some of our radio frequencies which we use to speak to aircraft.
"It only affects some parts of Scottish airspace and flights from and to some Scottish airports but there may be delays as a result this morning.
"We have identified the cause and isolated the problem and the situation is now improving."
Transport minister Derek Mackay said: "There was a technical issue that has been rectified and addressed, however there are knock-on consequences to the airlines.
"People should check with their airlines and the airports to ensure that their flights are running."
The CEO of a Belfast business centre has issued a stark warning to other businesses after being "held to ransom" by cyber criminals.
[NEXT_CONCEPT]
Scotland's busiest airports have returned to normal after a day of disruption caused by an air traffic control failure.