The Norwegian actor, who played Tormund Giantsbane in the HBO series, told people to "take care of each other, keep your distance and stay healthy".
Kristofer confirmed he had the virus and was self-isolating at home with his family.
On Instagram, he wrote: "Greetings from Norway! Sorry to say that I, today, have tested positive for COVID19, Corona virus. My family and I are self-isolating at home for as long as it takes. We are in good health,I only have mild symptoms of a cold."
"There are people at higher risk for who this virus might be a devastating diagnosis, so I urge all of you to be extremely careful; wash your hands, keep 1,5 meters distance from others, go in quarantine; just do everything you can to stop the virus from spreading.
"Together we can fight this virus and avert a crisis at our hospitals. Please take care of each other, keep your distance, and stay healthy!
"Please visit your country's Center for Disease Control's website, and follow the regulations for staying safe and protecting not just yourselves, but our entire community, and especially those at risk like the elderly and people with pre-existing conditions."