The Braves selected Wood's contract from Double-A Mississippi, giving the bullpen seven relievers.
The Braves went with six relievers on an 11-man pitching staff before the bullpen was stretched for seven innings in Wednesday night's 3-0 loss to Toronto.
Francisco, who had shared time at third base with Chris Johnson, was hitting .241 with five homers, 16 RBIs and 43 strikeouts in 108 at-bats. He hit .234 with nine homers when playing behind Chipper Jones in 2012.
The Braves have 10 days to trade, release or send Francisco outright to the minors. Manager Fredi Gonzalez said a trade is possible.
"It's tough," Gonzalez said. "It's a decision that wasn't made over a two-minute conversation. It took a long time to process the whole deal. The good thing about this for Juan and also for us ... two or three clubs called on Juan. There's a chance we trade him. There may be a possibility Juan gets to go to a major league club someplace else."
Francisco declined an interview request after being informed of the move.
Johnson, who is left as the primary third baseman, is hitting .346 with three homers and 14 RBIs.
Francisco was 0 for 3 and the Braves had 11 strikeouts in Wednesday night's loss. Three starters hitting below .200 were benched Thursday: outfielders B.J. Upton, .146 and Jason Heyward, .152, and second baseman Dan Uggla, .186.
"Sometimes it just helps to sit back and relax and watch the game, whether it's one game or whatever it is," Gonzalez said. "I suspect those guys are upset and that's good to see also. You don't want a guy who's happy about not playing. ... In the long run, those guys that are not playing tonight, we'll win a championship with those guys."
B.J. Upton, who signed a five-year, $75.25-million contract before the season, has the lowest batting average among all major leaguers with enough qualifying at-bats. He showed his frustration by throwing his bat and slamming his helmet to the ground after his second strikeout Wednesday night.
"I think at the end of the year B.J. will be our centerfielder," Gonzalez said. "I really believe that, but we need to get him going. We need to get him straightened out and get him going. And we will."
B.J. Upton took extra batting practice before Thursday night's game.
When asked how long Upton will be held out of the lineup, Gonzalez said "I haven't even put a timeframe on it."
Wood, a second-round pick from the University of Georgia in the 2012 draft, was 4-2 with a 1.26 ERA in 10 starts at Mississippi. He will join the Braves' bullpen.
The Braves have lost left-handed relievers Eric O'Flaherty and Jonny Venters to season-ending elbow injuries this year. Wood, who worked exclusively as a starter in the minors, joins Luis Avilan as left-handers in the bullpen.
Wood said the only time he has made consecutive appearances in relief was in spring training. He called his first opportunity in the majors "kind of indescribable, really. It's just an unreal feeling."
The Braves used four relievers Wednesday night. Starter Kris Medlen left the game after two innings with a contusion to his left calf. Gonzalez said Medlen had no swelling on Thursday and should make his next scheduled start.