Colvin remained in stable condition at Jackson Memorial Hospital in Miami, where he's expected to remain a few days for observation.
Baseball commissioner Bud Selig said he spoke with Colvin.
"Hopefully he's going home tomorrow," Selig said. "It scared me."
With Colvin on third base during Sunday's game against the Florida Marlins, Cubs catcher Welington Castillo hit a ball to left field. Colvin watched the ball, and he didn't see a large chunk of the shattered bat heading toward him. The bat punctured the upper left side of his chest. The team said there was minimal external bleeding, and he was being treated with a chest tube to prevent a collapsed lung.
"I want to thank Cubs fans for their support all season, especially right now, and let everyone know that I'm doing OK," Colvin said in a statement. "I also want to thank everyone who has helped take care of me here in Miami -- the Cubs and Marlins training and medical staffs, the EMTs at the ballpark and everyone here at the hospital."
The 25-year-old rookie will miss the remainder of the season. He hit .254 with 20 home runs and 56 RBIs.
"You never want to have a season end early, and I'm disappointed that I'm not going to be able to make it through the finish line with the rest of my teammates," Colvin said. "That being said, I couldn't be more thankful for the Cubs organization, my teammates and the opportunity to play for Cubs fans my rookie season. Thank you from the bottom of my heart."
After the incident, Castillo was worried about his teammate.
"I feel really bad about it," Castillo said. "It wasn't on purpose, but he's my teammate. I hope he's getting better."
Castillo was using a maple bat, which usually breaks into larger pieces when it shatters. Ash bats often splinter into small fragments.
"These bats, I'm amazed it doesn't happen more," Cubs manager Mike Quade said. "We have seen guys get hit with pieces, but to actually get stabbed with one, I just don't ever remember [seeing it]."
But Quade didn't suggest there was a controversy.
"I have no opinion on that right now," he said after the game. "Somebody with a better knowledge of physics, density of wood, I think would be better. I think players want bats that are lighter and maybe thinner. There's probably too many variables for me to have an opinion."
Cubs infielder Jeff Baker said he uses ash bats.
"I saw an umpire get slashed on the neck in Kansas City and it's just not worth it to me," he said. "I don't want that on my conscience if something happens and someone gets hurt. I just use ash and go from there."
Castillo said he has used maple bats his entire career.
"It wasn't my fault," he said. "I didn't want to hit him on purpose. That's just baseball. It happens."
Speaking at Yankee Stadium, Selig said baseball's record on broken bats had improved. Harvard and the University of Wisconsin are analyzing the issue.
"We're down over 50 percent on broken bats," Selig said. "We've been very vigorous in attacking the problem and we continue to be."
ESPNChicago.com's Bruce Levine and The Associated Press contributed information to this report.