All questions ask about the other way round, ie. can a virtual machine compromise the host. But I'm asking can a virus on the host machine compromise the guest virtual machine?
Yes, it can.
Any data stored on the virtual hard drives of the virtual machines is stored on the hard drive of the host system. When any VMs are in "suspended" state, their RAM content is also saved on the hosts hard drive. Any malware which can access these files can read and modify their content.
Another attack vector would be to target the hypervisor process directly and inject code into it. When one controls the hypervisor, one controls the virtual machines it executes.
A malware called Crisis has been spotted in the wild which targets virtual machine images on the machine it runs on. An attack from the host system circumvents most security features a guest system could have, which means that it would be almost impossible to harden a guest system against this kind of attack.
If a virus is on the host machine and operates as a normal/privileged user, and a normal/privileged user on that machine can use the virtual machine, there's nothing that prevents the virus from compromising private data from the virtual machine.
The security model of virtual machines does not protect or separate the guest from the host, quite contrary, access to the guest is facilitated in many ways: integration with the host (think VmWare unity), APIs that make guest management simple and automated, and shared resources (input devices, storage, etc.)
A virus you talk about is as unremarkable, so unremarkable that ends up being remarkable when it happens. There was a lot of media coverage when the first malware that infected virtual guests was first discovered in 2012.
When encountering a Windows-based PC, Crisis actively searches for VMware virtual machine images. When they're found, the malware copies itself onto an image using VMware Player.
It does not use a vulnerability in the VMware software itself, it takes advantage of an attribute of all virtualization software: namely that the virtual machine is simply a file or series of files on the disk of the host machine. These files can usually be directly manipulated or mounted, even when the virtual machines is not running.
Its aim is to get inside as many systems it can to steal the maximum amount of information.
The low number of infections and their wide geographic distribution could suggest that this malware is used in targeted attacks rather than widespread ones.