Satellite images taken on 14 February and published by Fox News appear to show two batteries of eight missile launchers and a radar system on Woody or Yongxing Island in the Paracels.
The presence of missiles would significantly increase tensions in the acrimonious South China Sea dispute.
China's Foreign Minister Wang Yi said reports were a Western media invention.
But Mr Wang defended "the limited and necessary self-defence facilities" on islands inhabited by Chinese personnel as "consistent with the right for self-preservation and self-protection.... under the international law".
Taiwan's defence ministry said it had "learned of an air defence missile system deployed" by the Chinese on Woody Island.
It would not say how many missiles had been deployed or when, but told the BBC they would be capable of targeting civilian and military aircraft..
The commander of the US Pacific Fleet confirmed the deployment to Reuters news agency.
Adm Harry Harris said such a move would be "a militarisation of the South China Sea in ways" China's President Xi Jinping had pledged not to make.
Japan's Chief Cabinet Secretary Yoshihide Suga said there were "serious concerns" over China's "unilateral move to change the status quo" in the region, and "we cannot accept this fact".
China has been carrying out extensive land reclamation work in the region, which it says is legal and for civilian purposes.
But the work has angered other countries which also claim the territory, and there is growing concern about the implications of the area becoming militarised.
The latest images of Woody Island were captured by ImageSat International.
They show a close-up of a section of beach, the shape of which resembles the northern coastline as it appears on other images, and point out two missiles batteries. Each battery is made up of four launchers and two control vehicles.
Two of the the launchers appear to have been erected, says the report.
An image taken of the site on 3 February shows the beach empty.
Fox News quoted a US defence official as saying the missiles appeared to be the HQ-9 air defence system, with a range of about 200km (125 miles).
What is the South China Sea dispute?
Rival countries have wrangled over territory in the South China Sea for centuries, but tension has steadily increased in recent years.
Its islets and waters are claimed in part or in whole by Taiwan, China, Vietnam, the Philippines, Malaysia and Brunei.
China has backed its expansive claims with island-building and naval patrols, while the US says it opposes restrictions on freedom of navigation and unlawful sovereignty claims - by all sides, but seen by many as aimed at China.
The frictions have sparked concern that the area is becoming a flashpoint with global consequences.
Although largely uninhabited, the Paracels and the Spratlys may have reserves of natural resources around them. There has been little detailed exploration of the area, so estimates are largely extrapolated from the mineral wealth of neighbouring areas.
The sea is also a major shipping route and home to fishing grounds that supply the livelihoods of people across the region.