The first thing to try would be a factory reset. Don't forget to back up your content and make sure your contacts and calendar are fully sync'd first. Doing this will reload your operating system from ROM and you'll need to set the phone up again. With luck, it'll solve the issue, even if it's malware. When you log back into Google, don't choose the restore option, but rather add your apps back one at a time. If the problem recurs, you'll have found the culprit if it's an app. If not, then whatever the cause was, it's gone.
