"Malware" is just short for "malicious software". Software is malicious if it was written with malicious intent, which is intent to cause harm. (Technically it doesn't even need to succeed at causing harm, or even have the capability of doing so, it just needs to have the intent of causing harm.

Therefore, by definition, if the machine that you are using is capable of running software (using whatever definition of software you care to use, and regardless of whether or not it is Turing Complete) it can run malware.

"Malware" is just short for "malicious software". Software is malicious if it was written with malicious intent, which is intent to cause harm. (Technically it doesn't even need to succeed at causing harm, or even have the capability of doing so, it just needs to have the intent of causing harm.)

Therefore, by definition, if the machine that you are using is capable of running software (using whatever definition of software you care to use, and regardless of whether or not it is Turing Complete) it can run malware.