Vizcaino left Friday night's 11-2 loss to the Colorado Rockies after throwing three pitches in the ninth. It was his first appearance since he missed four straight games with an infection on his right elbow.
Interim Braves manager Brian Snitker indicated that Jim Johnson, who had 101 saves for the Baltimore Orioles in 2012 and '13, will get the first chance to close. Snitker also might use rookie Mauricio Cabrera.
Johnson entered Saturday's game in the ninth with the score tied at 3. He gave up a leadoff single and threw two wild pitches as the Rockies went on to beat the Braves 4-3.
Reliever Eric O'Flaherty was reinstated from the disabled list to take Vizcaino's spot on the roster.
The team doesn't know how long Vizcaino will be sidelined.
"It's just time-consuming," Snitker said. "You've got to calm everything down until you don't feel anything before you start throwing again or you end up really screwing things up. You've just got be patient wanting to get back and get everything good again."
Vizcaino's hold on the job was tenuous before his latest injury. Though he has converted 19 of 23 save chances since the beginning of 2015, Vizcaino has a 5.11 ERA with 14 walks in his past 15 games.
In his first 23 games, Vizcaino went 1-0 with a 1.52 ERA and seven walks.
Snitker said the Braves, who own baseball's worst record, view Vizcaino as a long-term solution in the back of their bullpen.
"I talked to him a few weeks ago," Snitker said. "He's a huge part of what we're trying to do here. He's a young kid who cares a lot. What he brings is going to be valuable to the Atlanta Braves for a long time."
Vizcaino was suspended for the first 80 games last season after testing positive for stanozolol, a performance-enhancing drug. He had elbow ligament reconstructive surgery and missed the 2012 and '13 seasons.
O'Flaherty had a 1.50 ERA with no walks and eight strikeouts in six rehab appearances.
Information from The Associated Press was used in this report.