Mercedes reserve driver Stoffel Vandoorne, now driving for the German manufacturer in Formula E, and George Russell - who drives for Williams but is effectively on loan given he is a member of Mercedes' junior driver programme - are the main options to replace Hamilton in Sakhir.
Hamilton says he's been working hard to follow all of the COVID safety protocols - and wants his fans to know he wasn't taking stupid risks and being irresponsible.
Hamilton has already clinched the 2020 Formula 1 World Drivers' Championship with the team winning the constructors crown, in a season conditioned by the coronavirus.
Hamilton's positive test came a day after he won the Bahrain Grand Prix.
The 22-year-old Briton has tested several times for Mercedes but running him in Bahrain this weekend - as well as potentially the season-closing race in Abu Dhabi a week later if Hamilton does not recover in time - is a good opportunity for the team to assess his development in a competitive environment.
"I'm really lucky that I feel OK with only mild symptoms and will do my best to stay fit and healthy".
Formula One started a shortened 17-race season in July after the Australian opener in March was cancelled when a McLaren employee tested positive.
The Briton wrapped up his record-equalling seventh title in Turkey last month and picked up his 11th win of the season in Bahrain on Sunday.
"All contacts have been declared".
He left Dubai for Bahrain, where he had three further tests that all returned negative before it was confirmed on Tuesday he had contracted the virus.
"The Mercedes-AMG Petronas F1 Team regrets to announce that Lewis Hamilton has tested positive for COVID-19 and will be unable to take part in this weekend's Sakhir GP", said his team in a statement on Twitter.
Reserve driver Stoffel Vandoorne was already scheduled to travel to Bahrain after Formula E testing in Valencia.
The Silver Arrows are viewing a future with Russell to replace either Hamilton or Valtteri Bottas in the near future and they see it as a great opportunity to give Russell a try out with the current vehicle.