Jones suffered the injury during his at-bat to end the top of the fifth inning.
"I got a good pitch to hit and tried to come out of my shoes to hit it," said Jones. "And I'm a switch-hitter, it's something that's happened to me dozens of times."
Jones will be reevaluated on Monday morning, but Team USA manager Davey Johnson made it clear in his postgame news conference that he didn't expect to have Jones in the American lineup again in the near future.
"I think anytime somebody has a little strain in the spring, you have to be real cautious," Johnson said. "I doubt if he'd be available for a week or two."
With its 15-6 win over Venezuela, Team USA assured itself a berth in the second round of the Classic, beginning Saturday in Miami. The finals will be held at Dodger Stadium in Los Angeles on March 21-23, making it unlikely Jones would be available for either round.
Jones, for his part, is holding out hope that he could return after a couple of days of rest.
"I won't do a thing [Monday], maybe test it out on Tuesday during our workout, and, you know, I'll just have to wait and see," said Jones.
Jones was hitless with two strikeouts in three at-bats Sunday before being lifted in favor of pinch-hitter Ryan Braun, who grounded out during the United States' eight-run rally in the sixth. The veteran Braves slugger started both games for the United States, and has gone 0-for-7 with five strikeouts thus far in the tournament.
With Jones unavailable, Mets star David Wright will take over full time as the starter at third base for the Americans. Jones and Wright had alternated between third base and designated hitter in Team USA's first two games. Utility man Mark DeRosa, who had four RBIs on Sunday, will serve as Wright's primary backup at the hot corner.
"I told David Wright, it's probably the last time you are going to DH," Johnson said.
Ed Eagle is an editorial producer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.