The injury is similar to the one suffered earlier this spring by pitcher Jon Garland, who is expected to miss at least a month.
Although manager Don Mattingly didn't offer a timetable Friday for Navarro's return, it is likely Navarro will miss all of April.
Navarro, whom the Dodgers signed as a free agent last winter to be Rod Barajas' backup, felt something in his right side after taking a swing during batting practice Thursday and immediately stopped. He was sent for an MRI later that day.
But Mattingly also hinted that Barajas might draw almost all of the starts while Navarro is out. Although Barajas is 35 and Mattingly had planned to give him regular rest, that break presumably isn't as important in April.
"We're looking at Rod as the primary guy," Mattingly said. "I know I have to keep him strong, and I know he is an older guy. But I love his leadership. Earlier in the season, it isn't as big a deal. As you get more into summer, he will have more games under his belt and you're getting into some heat, so really, you're trying to keep him from breaking down."
Tony Jackson covers the Dodgers for ESPNLosAngeles.com.