Sickening footage shows a postman wipe his nose and rub it around a doorway while a person self-isolates inside.
The clip has been doing the rounds on social media, where viewers have expressed their outrage.
Royal Mail say they have "launched and urgent investigation" after viewing the footage, which appears to have been taken on a door camera.
The clip shows a postman approach the door, put a parcel through the letter box before wiping his nose with his left hand and then wiping it on a railing, the door handle, a wall and the letter box.
There is no indication of where the incident took place but he postman appear to be dressed in the distinctive Royal Mail uniform.
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Several people have shared the video on various social media websites and some have called for the police to investigate.
The Royal Mail have acknowledged the video publicly by replying to one person on Twitter, to say they were aware of the footage and were looking into it.
A spokesperson for Royal Mail told The Sun: "Royal Mail was very sorry to learn about this incident, and for any upset and distress it may have caused.
"We are in touch with the customer concerned and we are looking to offer them additional support. We have launched an urgent investigation and, once complete, appropriate action will be taken.
"Royal Mail takes the health and safety of its customers very seriously. We have already made a series of adjustments to our parcel handling procedures to offer our customers greater protection during this time.
"We expect the highest standards of behaviour from our people while out on deliveries and collections at all times. If any customer has any cause for concern, they should contact our customer service team with details so we can investigate."
Like other respiratory infections, coronavirus is spread by droplets from coughs and sneezes, with an incubation time from one to 14 days.
Health experts have urged people to reduce the risk of infection by regularly washing their hands with soap and water, covering their mouths and noses when they sneeze or cough, avoiding sharing food, drink and utensils.
