I have been looking around and doing some research on how to secure file uploads on Azure websites but every article I stumbled upon only mentioned about setting up antivirus on virtual machines. What I have is a website straight off the "Azure websites" function (not "Virtual Machines"), that you can publish and modify files via a provided FTP details. Is there an easy way to implement real-time antivirus security checks that trigger each time a user uploads a new file on the website?
Zen - there is no native virus scanning / anti-malware feature on Websites. As you have found the only way to enable this scenario would be to utilise either Web Roles in a Cloud Service or Virtual Machines. Microsoft recently made their anti-malware endpoint protection solution free on Cloud Services and VMs (see http://azure.microsoft.com/blog/2014/10/30/microsoft-antimalware-for-azure-cloud-services-and-virtual-machines/). Depending on your needs deploying to Web Roles may not be to far away from using Websites.