Jones is hitting .307 with five homers and 24 RBIs in his final season. He will retire after the season.
The loss of Jones could be a key blow to the Braves' hopes of remaining close in the NL East. The Braves are 19-5 when Jones starts and 7-16 in games he doesn't, including five straight losses before Saturday's game.
"If he misses six or seven in a row, we're in trouble," manager Fredi Gonzalez said before learning Jones went on the disabled list.
Boscan was hitting .192 with two homers at Gwinnett, started Saturday against the Washington Nationals.
The 40-year-old Jones missed seven straight starts before landing on the disabled list. He had a ground ball hit his leg on May 18 in Tampa Bay. His only appearance in a game since was a walk as a pinch-hitter on Wednesday night.
Jones had the hematoma drained by Dr. Marvin Royster on Saturday morning.
Juan Francisco started at third base against Washington's Stephen Strasburg after moving left fielder Martin Prado to third on Friday night. Gonzalez said he will decide if Francisco or Prado will be the primary third baseman the next two weeks.
"I'm not going to go back and forth," Gonzalez said of his options at third base, adding "Francisco can make that decision" with a good game.
The Braves have a pressing need at catcher after backup David Ross left Friday night's game with a right groin strain. Brian McCann took over for Ross in the second inning after missing the previous three games with an illness.
Gonzalez said McCann "really struggled" to make it through the final innings of Friday night's game.
Gonzalez said he even asked home plate umpire Doug Eddings to keep an eye on McCann and alert the Braves' dugout "if he looks faint."
Outfielder Matt Diaz is the team's emergency catcher.