The 26-year-old American won his first Major championship on Sunday when he edged compatriot Michael Thompson and Britain's Graeme McDowell by one stroke at the Olympic Club in San Francisco.
"I'm a guy who loves my family and...I have the rest of my life to play in The Open," Simpson told reporters.
"I don't want to miss the birth of my second child so it's an easy decision. I'd love to go and try to win another Major but in the grand scheme of things it's a decision I know I'll always be happy I made."
Simpson's victory at the weekend lifted him to fifth in the world rankings and up to third in the U.S. Ryder Cup points table ahead of the match against holders Europe in Illinois in September.
The Open, the year's third major, starts on July 19.