The Liaoning carrier and its flotilla of escorting frigates and destroyers were apparently on their way back to base in northeastern China from the South China Sea following training exercises, the agency reported.
The Chinese vessels moved through waters off Shantou in the southeastern Chinese province of Guangdong early Wednesday morning and continued north, CNA reported, citing the defense ministry.
The agency said the ships remained "west of the median line of the Taiwan Strait," or closer to mainland China.
By Thursday morning, the Liaoning carrier had completed its passage through the strait, the news agency reported.
Taiwan's President Tsai Ing-wen, who is in Nicaragua, has been briefed about the situation and requested that officials in Taipei closely monitor the movements of the Chinese vessels, CNA said.
Tsai drew anger from China
when she met senior US Republicans including Senator Ted Cruz in Houston on Sunday en route to Central America during a controversial transit stop that Beijing had asked the United States to not allow.
Relations between Taiwan, China and the US have been strained since President-elect Donald Trump spoke to Tsai in a phone call in December,
upending decades of diplomatic protocol.
China views Taiwan as a renegade province and, since 1979, the US has acknowledged Beijing's claim that Taiwan is part of China, with US-China relations governed by a set of protocols known as the "one China" policy.
Analysts said it was the second time China's aircraft carrier had navigated the strait, and, despite rising tensions between the two, the move shouldn't automatically be seen as provocative.
"China conducted the exercises in the South China Sea more for operational readiness purposes than political, although political is never out of the picture when the PLA Navy goes to sea," said Carl Schuster, a professor at Hawaii Pacific University and former director of operations at the US Pacific Command's Joint Intelligence Center.
The Liaoning carrier's J-15 fighter jets last month practiced air confrontations and air refueling
in the Yellow Sea late before the ship and its flotilla headed into the open Pacific beyond Taiwan and Okinawa.
China's state-run Global Times media agency published an editorial on Christmas Day, timed to coincide with the aircraft carrier Liaoning's maneuvers.
The piece called on China to build up its fleet of aircraft carriers, make them combat-ready, sail them to the eastern Pacific and look to set up naval supply bases in South America.
The Global Times also said the drill is a sign the Liaoning's combat capability has been enhanced and its areas of operation expanded, and could soon include the eastern Pacific. That would extend to the seas off the West Coast of the US.
The South China Sea is home to a string of messy territorial disputes
that pit multiple countries against each other.
Tensions have ratcheted up as China has reclaimed land in massive dredging operations, turning sandbars into islands equipped with airfields, ports and lighthouses.
Brunei, Malaysia, the Philippines, Taiwan and Vietnam all dispute sovereignty of several island chains and nearby waters in the South China Sea -- with rival claims to the Chinese interpretation.