The drills also come days after the US Navy's USS Antietam, a guided-missile cruiser, conducted a transit through the narrow waterway separating China and Taiwan.
China is holding military exercises in the East China Sea and the South China Sea near Taiwan this week, days after a defence white paper said Beijing would not rule out retaking the island by force.
The China Maritime Safety Administration issued notices on Sunday and Monday warning against entering broad swaths of airspace and waters off the coast of eastern Zhejiang and southern Guangdong provinces due to "military activity".
The announcements said drills in the East China sea were scheduled to run through Thursday and the ones in the South China Sea would end Friday.
But it did not offer details on the scale of the exercises or which military units were involved.
Beijing sees Taiwan as part of its territory awaiting unification, even though the two sides have been ruled separately since the end of a civil war in 1949.
The defence white paper published last week stressed Beijing's willingness to use force to thwart any move towards the self-ruled island's independence.
The drills also come days after the US Navy's USS Antietam, a guided-missile cruiser, conducted a routine transit through the narrow waterway separating the Chinese mainland and Taiwan.
Beijing reacted furiously after the US Congress greenlighted the potential sale of $2.2 billion worth of arms to Taiwan earlier this month and threatened sanctions on companies involved.
Relations between Beijing and Taipei have plummeted since President Tsai Ing-wen came to power in 2016 because her party refuses to recognise the idea that Taiwan is part of "one China".
As punishment, Beijing has cut official communications, ramped up military exercises, poached diplomatic allies and ratcheted up economic pressure on the island.