The San Francisco Chronicle said Mr Baker died in his sleep at his home in New York on Thursday night.
He initially designed an eight-colour flag in 1978 for the city's gay freedom day, the precursor to the modern pride parade.
A candlelight vigil is planned for Friday evening in San Francisco.
Screenwriter Dustin Lance Black tweeted: "Rainbows weep. Our world is far less colourful without you, my love. Gilbert Baker gave us the rainbow flag to unite us. Unite again."