Lewis' team, Mercedes, said it on Monday that the Briton woke up with mild symptoms and returned a positive result for a subsequent test and a re-test again.
The self-isolating Hamilton won the Bahrain Grand Prix on the same circuit on Sunday.
In due course, Mercedes says a replacement will be named.
"Apart from mild symptoms, he is otherwise fit and well and the entire team sends him our very best wishes for a swift recovery," a statement said.
On November 15, at the Turkish Grand Prix , Hamilton, 35, secured his record seventh world title.
Hamilton will miss his first F1 race on sunday since his debut at the 2007 Australian season-opening race.
Before returning to the racetrack, he must return the negative test and is therefore in question for the final race of the season in Abu Dhabi on 13 December.
Hamilton was tested three times last week, including at the Bahrain International Circuit on Sunday, Mercedes said and returned a negative result on each occasion.
Nevertheless, as well as waking up on Monday with mild symptoms, he was also told that a contact ''before his arrival in Bahrain" touch had tested positive.
Lewis Hamilton comes in as the third F1 driver after Sergio Perez and Lance Stroll, to have a positive coronavirus test this season.
Who will be the replacement for Hamilton for the Mercedes team in the paddock on sunday?
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