Artists including Kanye West, Maroon 5 and Rage Against The Machine have refused to perform in the state until the legislation is reversed.
The singer criticised the acts during his concert at the Tucson Arena on Thursday.
According to the Arizona Daily Star, John told the crowd: "We are all very pleased to be playing in Arizona. I have read that some of the artists won’t come here.
"They are f**kwits! Let’s face it - I still play in California, and as a gay man I have no legal rights whatsoever. So what’s the f**k's with these people?"