GANs are unsupervised machine learning algorithms. According to Wikipedia, unsupervised algorithms are :
Unsupervised learning is a branch of machine learning that learns from test data that has not been labelled, classified or categorized
In GAN networks, only training data is provided which is not labelled. The network generates candidates ( generative ) which are evaluated by the discriminator. The network slowly learns from the data given from a latent space.
Suppose, you want to create a GAN network which can make a Monet painting. You just need to feed it some Monet paintings. Here, you are not interested in classifying the painting, but copying/mimicking it.
Hence, there is no need for labels here which makes GAN an unsupervised machine learning algorithm.