"Post-op is an extremely vulnerable time and I think your employers would be very concerned for the privacy of any patients in your 'care'," she tweeted them directly.
Her fans flooded her with supportive messages, criticising the unnamed nurse for sharing private information about a patient on social media.
Responding to one fan, Szubanski posted: "Thanks. I have to say it was quite upsetting to find that in my feed. Made me feel very vulnerable and unsafe."
And in another, she added that she "bloody loves nurses and medical professionals" but was shaken up by the incident.
Others slammed the nurse in question, calling them "vile" and "unethical".
Another urged the star "not to let it go" given it is ultimately a legal issue.
Szubanski later thanked her fans for their messages, adding that if she decided to follow up on the matter, she'd do so "through the appropriate channels".