Patients have been needing urgent treatment at emergency units in Oklahoma hospitals after overdosing on the drug, Dr Jason McElyea says.
Small doses of Ivermectin are approved for use on humans, but not for Covid.
“You’ve got to have a prescription for this medication for a reason – because it can be dangerous,” Dr McElyea told the BBC.
He said a “handful” of people overdosing on the drug were putting further strain on hospital staff already stretched by a surge in Covid cases.
“The [emergency rooms] are so backed up that gunshot victims were having hard times getting to facilities where they can get definitive care and be treated,” he told local broadcaster KFOR earlier this week.
Ivermectin, mainly a veterinary deworming agent, can be used in small doses to treat some human conditions.
But the drug has become controversial after being promoted as a way of treating or preventing Covid, despite being so far unproven.
Its use has become so common in the US that the Food and Drug Administration (FDA) released a statement last month urging people not to take it.
“You are not a horse. You are not a cow,” the FDA said, warning that taking large doses of the substance “is dangerous and can cause serious harm”.
This week, the influential podcast host Joe Rogan, who has dismissed vaccines, said he was taking Ivermectin after testing positive for Covid-19.
Dr McElyea said patients who had taken the drug were arriving at hospital with vomiting, muscle aches, and even vision loss.
“Some people taking inappropriate doses have actually put themselves in worse conditions than if they’d caught Covid,” he told KFOR.
“You have to ask yourself, ‘If I take this medicine, what am I going to do if something bad happens?’ What’s your next step, what’s your back-up plan? If you’re going to take a medicine that could affect your health, do it with a doctor on board.”
Oklahoma is one of several US states battling the spread of the Delta Covid variant, with 18,438 new cases recorded in the past week.