Its first trip outside mainland China is part of the events marking the 20th anniversary of Hong Kong’s handover from Britain to China.
Its follows Xi Jinping’s visit last week, his first as Chinese president.
During his trip, which was marred by protests, he warned that any challenge to the Beijing central government was “impermissible”.
In 2014, Beijing said it would allow direct election of the city’s leader, but only from a list of pre-approved candidates. That led to mass protests – known as the umbrella demanding universal suffrage.
Mr Xi’s visit to the city came amid tight police security. Following his departure on Saturday, thousands of people marched in an annual event calling from more democracy.
It is accompanied by three warships, and will be anchored near Hong Kong’s Tsing Yi island for five days.
The 300m (990ft) aircraft carrier is a refurbished Soviet ship of the Kuznetsov class purchased from Ukraine and was built in the late 1980s.
It is part of a larger effort by Beijing to boost its military presence on the global stage.
In April, the country launched another aircraft carrier – its first to be made domestically. It is expected to be operational by 2020.