The base is in the far western reaches of Antarctica, close to the southern tip of South America.
Of the 36 infected, 26 are reported to be members of the Chilean military, while the others are believed to be maintenance workers.
The army said all were tested quickly and were being monitored by a medical team with the help of the health department.
“All present a favourable diagnostic and without any complication associated with the virus”, said the army statement quoted in several reports.
On December 17, Chilean media outlet La Tercera reported the crew of the Sargento Aldea had commenced a period of quarantine on the ship after three cases were recorded among the 208 crew.
The ship visited the base between November 27 and December 10, the report said.
For much of the pandemic there has been minimal travel to and from Antarctica as the continent sat in 24 hour darkness.
But transmission was always a risk, with a publication from The British Antarctic Survey (BAS) saying: “Given the diversity of transmission routes and vectors, preventing the introduction of the virus will be difficult, even with stringent quarantine procedures in place.”
Globally, as of today there have been 76,023,488 confirmed cases of Covid-19, including 1,694,128 deaths, reported to World Health Organisation.