Roberts told reporters that Kershaw is scheduled to play catch Saturday, and the left-hander will use next week's All-Star break to rest.
"Clayton had an MRI [Friday] morning and just like we expected, it was just inflammation," Roberts said. "He's going to start playing catch again [Saturday] and enjoy the break with his family. We'll figure out when in the second half we'll pencil him back in the rotation.
"... It was soreness. He's never had soreness in his elbow, so we wanted to check all the boxes and make sure there's nothing else to it. Fortunately, there wasn't."
Kershaw's last outing came against the Washington Nationals on Saturday, when he allowed three runs over four innings. He had three strikeouts and threw 54 pitches in the start.
The Dodgers placed Kershaw on the 10-day injured list with left forearm inflammation on Wednesday.
Kershaw, a three-time National League Cy Young Award winner, has a 9-7 record and 3.39 ERA over 18 starts this season. The 33-year-old left-hander has notched 127 strikeouts to just 19 walks over 106 1/3 innings.