Furcal received the news late Wednesday night and manager Joe Torre said Furcal left for the Dominican Republic at about 6 a.m. ET.
"He knows he takes as long as he needs," Torre said. "Hopefully we get him back soon and everything's OK. We'll just wait until he tells us."
Jamey Carroll took Furcal's place at shortstop and batted eighth for the series finale at Cincinnati on Thursday afternoon. With right-hander Bronson Arroyo starting for the Reds, Torre opted for second baseman Blake DeWitt, a left-handed hitter, at the top of the lineup.
"It's one of those things where you're around managing and you have things that come in the middle of the night," Torre said. "That was pretty much one of them, so hopefully he gets back to us at some point and he makes it to where he has to."
The Dodgers called up infielder Chin-lung Hu from Triple-A Albuquerque to fill Furcal's roster spot.