HMS Queen Elizabeth has set sail from Portsmouth after postponing its departure when crew members tested positive for Covid-19.
The Ministry of Defence (MoD) said fewer than 10 sailors had been affected and isolated in barracks ashore.
The aircraft carrier, which has a crew of 1,000, had been set to leave its base on Monday for training exercises.
The 65,000-tonne warship departed the naval base at about 16:35 BST.
Sailors who had contact with their infected crewmates had isolated onboard the £3bn vessel.
The Royal Navy said the positive tests were detected during "routine" preparations and those affected had worked with the NHS Test and Trace system "to ensure the virus does not spread further".
HMS Queen Elizabeth is the largest warship to be built in Britain and returned to Portsmouth for the first time as a fully-trained aircraft carrier in July.
The carrier is expected to carry out training exercises at sea before returning to base for supplies ahead of departing for major international exercises.