His team, Mercedes, said the Briton woke with mild symptoms on Monday and returned a positive result at a subsequent test and again at a retest.
Hamilton, who is now self-isolating, won the Bahrain Grand Prix at the same circuit on Sunday.
Mercedes say a replacement will be named in due course.
“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.
Hamilton, 35, clinched his record-equalling seventh world title at the Turkish Grand Prix on 15 November.
Sunday’s race will be the first Hamilton has missed since his F1 debut at the 2007 season-opening race in Australia.
He must return a negative test before returning to the paddock and therefore is a doubt for the final race of the season in Abu Dhabi on 13 December.
Mercedes said Hamilton was tested three times last week, including on Sunday at the Bahrain International Circuit, and returned a negative result on each occasion.
However, as well as waking with mild symptoms on Monday, he was also informed that a contact “prior to arrival in Bahrain” had tested positive.
Hamilton is the third F1 driver to test positive for coronavirus this season following Sergio Perez and Lance Stroll.
Mercedes have not said who will replace him but Belgian reserve driver Stoffel Vandoorne – the former McLaren F1 driver – will travel to Bahrain as planned after Tuesday’s Formula E test in Valencia.
News Source: BBC News