Satellite images taken on a couple of days ago and published by Fox News show two batteries of eight missile launchers and a radar system on Woody or Yongxing Island in the Paracels.
Taiwan, which also claims the island, confirmed the deployment.
But China’s Foreign Minister Wang Yi said the reports had been a creation of the Western media.
The presence of missiles would significantly increase tensions in the acrimonious South China Sea dispute. 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 deployment came as U.S. President Barack Obama called for the halt of the militarization of the South China Sea at the close of a meeting with Southeast Asian leaders in California.
Obama pressed for a “halt to reclamation, new construction and militarization” of Asia’s oceans, an indirect reference to China’s rapid construction in the South China Sea.