The Luther star has said he "feels okay and currently has no symptoms" but has been isolated since he found out he might have been exposed to Covid-19.
Elba, 47, said he has been isolated since finding out he was exposed to the virus.
"Stay home people and be pragmatic," he said. "I will keep you updated on how I'm doing. No panic."
Elba, who posted a video also featuring his wife Sabrina Dhowre, said she has not been tested and is "doing okay".
He said he got tested after finding out on Friday that he had been in contact with someone who had the virus.
"This is serious," he said before adding: "Now is the time to really think about social distancing, washing your hands."
Elba also urged his fans to remain "really vigilant".
He is not the first high-profiles actor to openly speak about being diagnosed with the virus.
The Oscar-winning actor, 63, has been in Australia filming an upcoming Elvis Presley biopic and said he started experiencing symptoms of the virus.
Hanks said he felt like he had a cold, singer Wilson, also 63, suffered from chills.
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