Following a meeting of the Government's Cobra contingencies committee, Ms Rudd said more than a million patients had been treated in the course of Monday.
"It is important to note that the vast majority of NHS organisations report that they are running contemporary IT systems, which are commissioned depending on local need", the NHS said in a statement.
Scottish targets included 11 health boards, NHS National Services and the Scottish Ambulance Service.
Terming such cyber-attacks as a shared responsibility between tech companies and customers, the tech giant said, so many computers remained vulnerable even two months after the release of a patch.
Digital managers in Britain had been bracing themselves Monday for a possible second cyber attack, but in the event there was no new attack.
As people across the globe returned to work, Japan reported 2,000 computers at 600 locations had been affected, with firms including Hitachi and Nissan reporting problems.
Numerous nearly 8,000 doctors' surgeries in England were also affected, warning of delays as doctors reverted to paper records and appointments.
Manchester United reveals £3.8m net loss for third quarter
Crystal Palace thumped Hull 4-0 at home last time out, putting an end to a losing run of three games without scoring. Southampton struggled to relieve the pressure building on manager Claude Puel against an under-strength United.
Yesterday, Jeremy Hunt told the BBC the National Crime Agency was investigating the incident that saw NHS computers locked down and money demanded from the attackers to unlock the files.
'It might be that they're just being very quiet because they don't want to instil a lack of trust in their system, ' she said.
At Broomfield Hospital, part of Mid Essex Hospital Services NHS Trust (Midlands & East), trauma patients are being diverted to Southend University Hospital.
"There are things you can do that everyone can do (.) in particular making sure that our data is properly backed up and making sure that we are using the software patches", he said.
Furthermore, the latest ransomware attack - believed to have come from a flaw in Microsoft's Windows software that the the US National Security Agency used to build a hacking tool for its own use - highlights the need for health services to introduce a comprehensive back-up plan and recovery processes in the event of a cyber-security breach.
Rob Whiteman, CIPFA chief executive said: "The NHS ransomware attack needs to be a stark reminder for all government organisations to ensure IT security is optimal, regularly reviewed and upgraded, and given the resources to match our reliance on digital systems".