Jones said he will not be able to play in the two remaining games against the Rays.
"It's safe to say my career in Tampa Bay is officially over," said Jones, who had planned to have family and friends from his hometown area in Deland, Fla., attend the game on Saturday.
Jones attempted to field the hard-hit, one-hop shot by Upton by quickly dropping to his right knee. But the ball skipped by his glove and ricocheted off his left calf. Upton reached base for a single.
Jones stayed down on the ground for about two minutes while Braves head trainer Jeff Porter examined him.
Jones talked with Porter and manager Fredi Gonzalez for a brief moment before nodding his head to say he was fine to continue playing.
The bruise stretched about five inches in diameter and was centered between the inside of his left calf and the top of his ankle. Jones said he did not feel it was necessary to be examined with an X-ray or MRI.
"It's fine," said Jones, who missed the first four games of the season after undergoing surgery to repair a torn meniscus in his left knee suffered on March 26. "I'd know if I needed one."
Jones decided to come out of the game after realizing he wasn't going to be of much use on the defensive end of things.
"It started getting worse and worse, and I finally told [Gonzalez], 'You better get somebody in there,'" Jones said. "It's hard to stay on the back side when you're trying to hit. Then, I knew I was going to be a liability in the field."
Following the seventh inning, Juan Francisco replaced Jones in the lineup as a pinch-hitter and took Jones' spot in the field.
Chris Girandola is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.