It really depends. For the most part, malware is designed to work on specific environments so while it's possible that you get something running under wine it's unlikely to affect the underlying Linux system. Although, there's never a 100% safe system so even this could be possible.
Because of that I would encourage to take some steps before downloading, installing or running anything, regardless of the operating system:
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Don't download random stuff from the internet. Clicking on buttons from websites you've never seen or heard of before is a great way of undermining your security. Try to download from official sources and read any installation instructions provided.
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Once you've downloaded something, the first thing to do is to verify the integrity of the data. Most products these days will (or should) publish a list of checksums; you can think of this as unique fingerprints. Here, you can see an example for ZorinOS. If the checksum that you download does not match the one published online, do not use it. Even if it's off by a single character.
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Another thing to do before installing or running anything is to scan for known malware signatures. For Linux, I recommend something called ClamTK, which I personally like to run manually on every file I download but you can also leave it running in the background. You may also upload that file to Virus Total for additional examination. Take a look at this, too:
In summary, it's not worth running an anti-virus for something that already runs in isolation, like Wine, and you have already examined thoroughly. But if you want, you can.
My personal preference is, when I suspect something is fishy, run it within a virtual machine. That way I can destroy it in two clicks if something goes wrong, as if nothing ever happened. On the Software Store you can install Virtual Box to start working with virtual machines.