"It sucks," the 47-year-old said in a clip, saying he got tested Friday because he realized he'd had exposure from someone who also tested positive.
"Listen, I'm doing okay," Elba said, before telling fans "this is serious."
"Now's the time to really think about social distancing, washing your hands," he continued. "There are people out there who aren't showing symptoms and that can easily spread it.
"Transparency is probably the best thing for this right now."
Elba encouraged anyone who felt ill to hunker down and get a test if possible, while also voicing solidarity with others who have the virus that's left at least 175,530 people infected, with 7,007 deaths worldwide.
The Wire star also extended condolences to those who've lost close ones or who have lost their economic livelihoods as businesses across the globe shut down.
"We live in a divided world right now, we can all feel it," Elba said. "But now's the time for solidarity. Now's the time for thinking about each other."
Elba joins fellow actor Tom Hanks and his wife, actress and singer Rita Wilson, on the list of celebrities who have tested positive for the virus.
The Hollywood pair is currently in quarantine in Australia.