Pedroia, 36, suffered a setback with his left knee injury in late January. Over the past two seasons, the Red Sox fan favorite has played just nine games, collecting three hits in 34 plate appearances.
Over the past several years, Pedroia has been a regular under the knife. In October 2017, he underwent a cartilage restoration procedure, followed by scar tissue removal in July 2018. Most recently this past August, Pedroia underwent knee joint preservation surgery, an alternative to knee replacement.
Earlier this month, new Boston manager Ron Roenicke said Pedroia wouldn't report to spring training with the rest of the position players.
"When a guy just ages and then he's not as good, that part's easy to see. But not a guy who has an injury and because of it has not been able to perform," Roenicke said at the time. "That part is really difficult."
Through his 14-year career in the majors, Pedroia has hit .299/.365/.439 with 140 homers, 394 doubles and 725 RBIs while collecting four Gold Gloves and earning MVP honors in 2008, when he hit .326/.376/.493 with 17 homers and 83 RBIs.
Valdez, 28, made his major league debut for the Texas Rangers last season and had a 3.94 ERA in 11 relief appearances. He was claimed off waivers by the Mariners from the Rangers in November.
ESPN's Joon Lee contributed to this report.