Varon, who leads the hospital's coronavirus unit, was dressed in full personal protective equipment (PPE) when he stopped to wrap his arms around a man being treated in the hospital's intensive care unit (ICU).
The photograph, taken by a Getty photographer, quickly went viral as the United States continues to see more than 100,000 newly diagnosed cases of COVID-19 daily.
"He was very sad because he's in a room where he knows nobody," Varon told "Good Morning America" of the patient, who was not identified. "We come in dressed like astronauts, and even though I usually have my picture with me so they can know who I am when I go to see them, it's very frustrating for the patients, and he was very emotional."
"And just when I heard [his emotion], I hugged him," Varon added.
Varon said the journey of fighting COVID-19 has been taxing not just for patients, but for medical staff like himself. He described working around-the-clock, day after day to care for patients.
"My days can be 16 hours ... and then when I get home, I get a million phone calls in the middle of the night," he said. "When I leave my home, I tell my wife, '[I'll] see you,' but I don't know when or what time. Sometimes I don't come back home the same day."
Hospitalizations of COVID-19 patients in the United States reached an all-time high of 93,238 on Sunday, according to the COVID Tracking Project. Current COVID-19 hospitalizations have gone up nearly every day since Oct. 25.
As the number of cases and hospitalizations continues to rise, Varon said he is particularly frustrated by people not practicing COVID-19 safety guidelines, including wearing a face mask and social distancing.
"We're frustrated because we see people, they come in very, very sick and when you ask them, 'How did you get [COVID-19]?,' they basically tell you that they didn't follow any of the things that we've been asking them to please follow -- no social distancing, no wearing masks, going to large gatherings," he said. "And then just coming to us near death."
"We are exhausted. We are tired," he said of his fellow doctors and nurses. "I have nurses [who] are in the middle of the day crying because they keep on getting patients and there are just not enough nurses that can help us."