Hamilton, who has already secured a record-equaling seventh world title and won Sunday's Bahrain Grand Prix, was experiencing mild symptoms, but was otherwise fit and well, his Mercedes team said.
"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 program," the Formula One champions said in a statement.
"However he woke up on Monday morning with mild symptoms and was informed at the same time that a contact prior to 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 35-year-old Briton was isolating according to local health guidelines, the team said, with a replacement driver to be announced in due course.
The Sakhir Grand Prix takes place on Dec. 6.