"In the light of the moon, holding on to a good star, a painter of rainbows is now travelling across the night sky," a family statement said.
Carle's most famous book, which tells the story of a ravenous caterpillar, was published in 1969 and has sold more than 50 million copies.
"For many years, my publisher and editor and I did not know the reason for The Very Hungry Caterpillar being so popular," he said.
"But over time, I've come to feel that it is a book of hope. And it is this hopeful feeling that has made it a book readers of all ages enjoy and remember."
Born in upstate New York to German immigrant parents, Carle moved as a child with his family to Stuttgart in the mid-1930s because his mother was homesick, only for his father to end up drafted into the army during World War Two and get taken prisoner by the Soviets.
He eventually moved back to New York and worked as a graphic designer and then at an advertising agency, before collaborating on his first picture book Brown Bear, Brown Bear, What do you see?