Montgomery, Stanford's leading receiver with 61 catches for 604 yards and three touchdowns, left last weekend's game against California with what Shaw described as a right shoulder sprain following the 38-17 victory. Shaw said he remains hopeful that Montgomery would return to play in a bowl game.
"Ty will be out of this game," Shaw said during Tuesday's Pac-12 coaches' teleconference. "He will not play this game and hopefully we'll get him ready for the bowl game, which looks like a distinct possibility."
Shaw said Montgomery made an effort to insert himself into Stanford's lineup this week, but the staff determined the "prudent" course of action would be to hold him out of Friday's game. Montgomery does have an injury history on the shoulder.
X-rays on the shoulder came back negative Saturday, and Montgomery was scheduled to undergo an MRI this week.
Friday's game has significance in the Pac-12 standings. While Oregon has already secured the North Division, UCLA would win the South with a victory over Stanford. Should the Cardinal win, the winner of Friday's Territorial Cup between Arizona and Arizona State would win the division and face the Ducks in the Pac-12 championship game.
ESPN.com's David Lombardi contributed to this report.