Stricker’s spots have gone to Daniel Berger, Harris English, Tony Finau, Xander Schauffele, Scottie Scheffler and Jordan Spieth.
They join automatic qualifiers Dustin Johnson, Collin Morikawa, Justin Thomas, Bryson DeChambeau, Brooks Koepka and Patrick Cantlay on the home team.
Berger, English, Schauffele, Scheffler, Morikawa and Cantlay are all rookies, making it the most newcomers on a US side since Stricker was among those blooded by Paul Azinger on a winning team at Valhalla in 2008.
Reed, who has previously featured in every American team since 2014, has been overlooked after he only returned from bilateral pneumonia at last week's Tour Championship in Atlanta.
Of the six picks, only Berger and Schauffele finished ahead of him in the PGA Tour’s season-ending event at East Lake, but that has been overlooked by Stricker.
“That was a very, very difficult call,” said Stricker of Reed. “I lost sleep over that one. He is a tremendous competitor. He plays well in matchplay.
“His record in the Ryder Cup is pretty darn good. It was not an easy one. But it was his health and the lack of play down the stretch that led to the decision. He took it like a true champion.”
Spieth will be playing in his fourth consecutive Ryder Cup, the longest current streak among the American contingent, while Furyk played on the defeated US team in Paris three years ago.