The right-hander, who had been pitching for the Cardinals, died in an auto accident in St. Louis on Sunday morning. Sunday night's Cardinals-Cubs game was postponed.
Prior to Sunday's Red Sox-Yankees game in New York, public address announcer Bob Sheppard announced the news of Hancock's passing, and a moment of silence followed.
"It's alarming," said Red Sox captain Jason Varitek. "It gives you a lot of thoughts about just having the opportunity to be here on earth. You reach out to his family and everybody that's close to him. It's just tragic."
The Red Sox released the following statement:
"The Boston Red Sox express our heartfelt sympathies to the family of Josh Hancock. Our thoughts and prayers are with his family and the St. Louis Cardinals, and we join all of Major League Baseball in mourning his loss."
After going 0-1 with a 3.68 ERA in those three outings for the Sox, Hancock was traded to the Phillies for Jeremy Giambi prior to the 2003 season.
Manny Ramirez, Varitek, Doug Mirabelli and Tim Wakefield are the four holdovers from Hancock's brief time with the Red Sox.
"He had a great start for us and kind of got himself going, and then we ended up trading him that winter," Varitek said. "But he did a phenomenal job and he was a huge part of St. Louis' success last year. He was a great guy. He was a good pitcher. I didn't know him extremely well. I liked his demeanor on the mound."
First baseman Kevin Youkilis played with Hancock at Double-A Trenton in 2002 and later that same year in the Arizona Fall League.
"It was kind of shocking when I found out today," said Youkilis. "It was really tough, just more of a shock. I'm still shocked right now. It's just a sad story. I haven't really heard what the whole details are of the whole thing. It hasn't really hit home yet. To all of his family and his friends out there, you just have to say a prayer for them and hope they handle it all right. The St. Louis Cardinals lost a good pitcher today."
Youkilis is just happy that Hancock was able to achieve some of his goals during a life that ended too soon.
"He always had good stuff," Youkilis said. "He was like an ace in the Minor Leagues. Josh was just one of those guys out there who just loved playing ball. He loved pitching and loved playing. Going out with a World Series and making the Major Leagues was a huge accomplishment, which was really good."
The Red Sox will have a moment of silence for Hancock prior to Tuesday's game against the A's at Fenway Park.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.