The information privacy company is offering services to specifically protect against reputational damage, account jacking and ID theft, the 'Daily Mail' reported.
Hacking of users accounts on Facebook, Twitter, LinkedIn and other social media sites are quite common, where another user logs in and posts derogatory or offensive messages, and can cause huge damage to an individual or business's image.
Justin Basini, CEO of the company providing the service, ALLOW, said that insurance "perhaps wouldn't have been needed a few years ago."
"That's all changed now. Every internet user faces a certain level of risk that one day a digital criminal will target them or that they will suffer damage to their reputation," Basini said.
The cover, at a cost of 3.99 pounds a month, will pay for legal advice and support if someone suffers an on-line attack and seeks some form of redress.
The insurance includes the cost of disabling accounts, suppressing offensive material and stopping any legal action triggered by hacking, for example if a hacker posts illegal material under a victim's name, the paper said.
It is available via the ALLOW Protect service, which also allows users to monitor how their personal data is used on-line, it added. On-line abuse and identify theft are so common that social media users are being sold specialist insurance to help protect their reputation.