The seven-time Formula One world champion is in isolation after his positive result was announced on Tuesday morning.
Hamilton will have to isolate in his hotel room for 10 days, putting in doubt his participation at the season finale in Abu Dhabi a week on Sunday.
An F1 statement said: “The FIA, Formula One and Mercedes Team can today confirm that during mandatory pre-race PRC testing for the Sakhir Grand Prix, Lewis Hamilton has tested positive for Covid-19.
“In accordance with Covid-19 protocols, he is now isolating. All contacts have been declared. The procedures set out by the FIA and Formula One will ensure no wider impact on this weekend’s event.”
Hamilton’s Mercedes team said Hamilton, 35, reported “mild symptoms” on the morning following Sunday’s Bahrain Grand Prix where he claimed his 11th win of the season.
“Lewis was tested three times last week and returned a negative result each time, the last of which was on Sunday afternoon at the Bahrain International Circuit as part of the standard race weekend testing programme,” a statement from the Formula One team read.
“However, he woke up on Monday morning with mild symptoms and was informed at the same time that a contact prior to his arrival in Bahrain had subsequently tested positive.
“Lewis therefore took a further test and returned a positive result. This has since been confirmed by a retest.”
The Mercedes statement continued: “Lewis is now isolating in accordance with Covid-19 protocols and public health guidelines in Bahrain.
“Apart from mild symptoms, he is otherwise fit and well, and the entire team sends him its very best wishes for a swift recovery.”
Hamilton posted videos to his Instagram account last week playing tennis with his father Anthony and running along a beach.
In another video, the Mercedes driver could be seen travelling in the same car alongside Anthony and his friend Daniel “Spinz” Forrest.
While both his father and Forrest were wearing masks, Hamilton did not have a face covering on.
Hamilton, who wrapped up his record-equalling seventh world championship in Turkey last month, is the third driver to have contracted the illness.
Sergio Perez missed the British and 70th Anniversary Grands Prix at Silverstone in August, while his Racing Point team-mate Lance Stroll also tested positive following October’s Eifel Grand Prix in Germany.
Sunday’s race will be the first Hamilton has missed since his debut at the 2007 season-opening race in Australia.
Mercedes have yet to confirm who will replace the Englishman for Sunday’s grand prix on the Outer Loop of the Bahrain International Circuit.
Mercedes reserve driver Stoffel Vandoorne, formerly of McLaren, is in the running, while the world champions could also turn to British driver George Russell.
Russell, 22, is in his second season with Williams, but is a member of the Mercedes junior driver programme.
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