If I'm designing a web application that allows people to upload files to scan them for vulnerabilities do I need to worry about the server that accepts the files being infected/corrupted if a malicious file is uploaded? Or will it be fine as long as the file is only scanned and not opened? If there is any danger in accepting these files what measures should I take to protect myself?
You have very good odds if the file is only scanned and not opened, but there have been instances of malware activating flaws in scanners.
Setup your scanner system to run non-persistently. A golden VM copy can be spun up pretty quickly for each scan instance. That way even if compromised it's only momentary.
Granted it's not impossible to also compromise the host under the VM, but compromising the scanner, the VM, and the Host is a pretty high bar.
Any application that accepts unrestricted file upload is subject to being exploited, if not properly secured.
OWASP has a really nice article on this subject, with a whole section regarding security practices you can use to protect your app.