Matsuyama split his opening two matches this week at Austin Country Club and needed to beat Max Homa (32) on Friday to force a play-off and determine who advanced to the knockout rounds.
As a result of Matsuyama's withdrawal, world number six Homa advances out of the group stage with a 3-0-0 record.
"I experienced some stiffness in my neck this morning while warming up on the range, preventing me from making a full swing," Matsuyama said in a statement.
"As a precautionary measure, I decided to concede my match to Max and rest before moving onto the Valero Texas Open next week."
This week's event marked the first PGA Tour start for the Japanese world number 20 since his fifth-place finish at The Players Championship.
Matsuyama also withdrew from last year's Valero Texas Open midway through his second round with a neck injury, less than a week before he was set to begin his Masters defence.
