Malware can only be executed if something loads it and executes it. Malware in the form of a Windows program will not run unless you boot Windows or you run a Windows emulation layer on Linux. In the latter case, it's unlikely (but by no means impossible) that the malware will have enough privileges to do harm.
It is however possible for malware to come with Windows but run outside of it, Windows being here the platform of the malware installer but not the platform of the malware itself. The malware could lodge itself in your hard drive's boot sector or could even infect your BIOS or other firmware.
It's also possible for malware running under Windows to access your Linux drive (unless it isn't physically plugged in) and plant Linux malware there.
These threats are not very common. Linux compatibility is not a feature that most malware authors aim for, and there isn't much hardware-infecting malware in the wild. In practice, such malware is unlikely to arise in the form of an untargeted attack. Targeted attacks are a different matter; if you're concerned about the NSA spying on you, get new hardware (among other precautions).