Ubuntu installed alongside an infected Windows system

The safest option would be to install Ubuntu on a different partition, but according to this post it seems safe. Here I quote it:

Wubi will not be affected by Windows viruses. Wubi is almost identical to the standard Ubuntu installation, except for the fact that everything is inside a file on the Windows partition. Therefore it cannot run windows executables (including viruses). The only way you can get a virus from Wubi is if you download something containing a virus, transfer the file to Windows, boot Windows, and then run the virus from Windows.

Also see this thread

EDIT Also if you want to run any programs in wine from your infected Windows installation, especially as root, you may open your system to infection. Also, the safest option is to format everything and then install Ubuntu - ObsessiveFOSS

Knowing of malware that are malicious beyond imagination I would just be too afraid to let anything even remotely touch my Ubuntu. Therefore a Wubi installation can not be recommended.

As already said Windows malware will not infect your Ubuntu OS or replicate through Ubuntu but there are a lot of trojans that are capable of changing or even encrypting files on your harddisk. If this file was your Ubuntu Wubi container then you will not only have lost Ubuntu but also you will have lost the opportunity to rescue data from the infected system. This could easily be done from Ubuntu installed in a separate partition and using file system that is not accessible from Windows or Windows viruses.

Therefore I strongly recommend a dual boot setup for running Ubuntu alongside a possibly infected or badly protected Windows.