Devastating Malware attack

My webhosted domain from which I run 3 WordPress websites is behaving as though it has been contaminated with malware.

Basically, if one approaches the sites directly via the url then everything is fine. HO]owever, if the site is approached via a link on another site (eg via Twitter, Facebook or a Google search) then the local user’s browser will experience a false screen declaring that the local computer is infected with a number of viruses and encouraging (virtually forcing) the user to download software that will clear the infection.

I understand from various anti-malware sites that the rogue malware deposits files on the users machine and hopes that they will purchase their software to clear the problem.

Is this a security leak in WordPress or have I just been careless and let in a hacker?

Following the advice of my webhost I am currently copying my entire domain to a local computer and will then treat that with a trusted anti-malware/virus app.

Any other advice out there?

Will Chapman