The official would not identify which systems but said no federal government entities were hit.
The cyber attack which hit the NHS was a ransomware attack which encrypts files on a user's computer, blocking them from view and threatening to delete them unless a payment is made.
"One customer said they actually forgot they were being robbed". Businesses need to patch to be completely protected, but Hickey's solution works for organizations that might need more time to upgrade.
"These people went through great lengths to create this malicious software so it would be foolish to assume this is their only attempt to do so", said Alex Holden, the chief information security officer at Hold Security LLC.
Companies and governments spent the weekend upgrading software to limit the spread of the virus.
The attack, known as "WannaCry" had a major impact across Asia as workers there returned to work on Monday, with Chinese state media saying nearly 30,000 institutions there had been infected.
"The message to patients is clear: the NHS is open for business".
It was too early to say what the overall cost of the attack to the public purse would be, the spokesman said.
Though Microsoft released a security update in March to patch the vulnerability on modern versions of Windows, the company quickly released another security update this weekend to address the security exploit on Windows XP, 8 and Server 2003.
Infected computers appear to largely be out-of-date devices that organisations deemed not worth the price of upgrading. Machines that contained the patch are much less at risk than those that didn't.
Labour has accused the Government of a "chaotic" response to the cyberattack, and claimed cuts had left hospitals "wide open" to being compromised.
In just one example, past year officials with the Lansing Board of Water and Light revealed they paid hackers $25,000 to unlock its communications system.
Hospitals and clinics were forced to turn away patients on Friday after a mass-distributed ransomware virus caused them to lose access to their computers.
WannaCrypt's victims included the National Health Service, Spain's Telefónica and numerous other organisations across the world.
Home Secretary Amber Rudd is due to chair a meeting of the Government's emergency Cobra committee on Whitehall at 5pm on Monday.
These ranks work with law enforcement agencies and governments around the globe through Microsoft's Threat Intelligence Center and Digital Crimes Unit.
How to prevent WCry attack?
"If a system supports some kind of critical processes those systems typically are very hard to patch".
Paying ransom will not ensure any fix, said Eiichi Moriya, a cybersecurity expert and professor at Meiji University.
Affected bodies included a social security department in the city of Changsha, the exit-entry bureau in Dalian, a housing fund in Zhuhai and an industry watchdog in Xuzhou.
Elsewhere in Asia, the impact seems to have been more limited.
Jim Beagle, president of data management firm Bridgehead, which has a number of NHS clients, said: "I think that the speed with which most NHS facilities got back up and running is testament to the robust processes for disaster recovery that they had in place".
European authorities have a warning for everyone hit by the worldwide cyberattack: Don't pay the ransom. No major Indian corporations reported disruptions to operations.
How to stop the attack from affecting your system? Primary care organisations across the north east of England are said to be now locked out of their IT systems, forcing doctors and nurses to improvise services without any computers.