Turner suffered a non-displaced fracture in his wrist when he was hit by a pitch during a spring training game Monday night against the Oakland Athletics.
Roberts did not reveal a timeline for how long Turner will be sidelined, although the Dodgers' manager acknowledged Monday night that "weeks are involved when you're talking about a fracture of any sort."
Turner told MLB.com on Tuesday that his wrist will be in a brace for a few days before he can start range-of-motion exercises, saying that avoiding surgery is "good news."
With Opening Day just nine days away, the Dodgers seem likely to slide Logan Forsythe to third base in Turner's absence, with Chase Utley and Kike Hernandez splitting regular duty at second base.
Turner, 33, batted .322 with 21 homers and 71 RBIs last season.
Turner breaks wrist on hit by pitch
Justin Turner gets hit by Kendall Graveman's pitch on his left wrist in the first inning and leaves the game with a broken wrist.
Buster: Turner's injury a big deal to Dodgers
Buster Olney explains how Justin Turner's wrist injury impacts Los Angeles' lineup.