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4 year oldHamilton, 35, was at an event in London earlier this month with Elba.
Sophie Grégoire Trudeau - wife of the Canadian Prime Minister Justin Trudeau - was also in attendance and has been diagnosed with coronavirus.
"I want to let you know that I am doing well," Hamilton said in a statement.
The Mercedes driver added: "There has been speculation about my health, after I was at an event where two people later tested positive for coronavirus.
"I have zero symptoms and it has now been 17 days since I saw Sophie and Idris. I have been in touch with Idris and happy to hear he is OK.
"I did speak to my doctor and double checked if I needed to take a test but the truth is, there is a limited amount of tests available and there are people who need it more than I do, especially when I wasn't showing any symptoms at all."
Hamilton said that he had been in isolation since last Friday - shortly before last weekend's season-opening Australian Grand Prix was cancelled because of the pandemic.
The Formula 1 season has been delayed until at least the start of June, with several races either postponed or cancelled.
— Lewis Hamilton (@LewisHamilton) March 21, 2020
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