Oxfordshire County Council and Oxford City Council have been taken offline while they investigate a "known issue, affecting websites globally".
This is linked to what the National Cyber Security Centre has described as a "critical security issue".
Organisations that run websites using a programming language called PHP were today warned to apply "temporary mitigations" or take systems offline until they could do so.
The issue could allow attackers to corrupt sites and exploit them.
The US cyber security agency warned that "vulnerabilities often provide a direct path to the server's file system or database".
The issue has seen the Finnish Government, the Netherlands ' cyber-security agency, parts of Wikipedia, and the online homes for some BBC programmes, including Doctor Who and The Traitors, offline.
Oxfordshire County Council's main website, where residents can access services, including parking and traffic filter permits, library accounts, information, care, and community support, has been taken down.
It has made a temporary website "to help with urgent matters such as safeguarding, schools, permits, and HWRC bookings".
A spokesperson for the council said: "our regular URL will redirect to this site:
Before the temporary site was created, attempting to access the county site resulted in an error and a Google warning: "attackers might be trying to steal your information", "for example, passwords, messages or credit cards".
In a statement, the council said: "Oxfordshire County Council have taken multiple web services offline due to a known global issue whilst we work to resolve the situation."
It added: "Our centre is open for urgent issues on 01865 519800 but call volumes are likely to be busy, so please us at a later date if your issue is not urgent."
The city's website, which can be used for paying council tax, business rates, planning applications, housing, bins and leisure services, is also offline.
The city council has shared a social media update where it says the situation "is not a cyber incident".
It said: "Oxford City Council's website is temporarily unavailable.
"This is a precaution because of a worldwide issue with the underlying technology and is not a cyber incident.
"You can still us by phone on 01865 249 811"
A fix has been shared for PHP issue.
The National Cyber Security Centre said: "Organisations using any version of PHP are affected and all organisations are highly encouraged to update to the latest fixed version.
"Organisations using older versions of PHP are highly encouraged to update to a fully supported version."
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