Nelson (elbow) was placed on the 60-day injured list Friday.
Nelson joined the Dodgers on a major-league deal Tuesday despite the fact that he's working his way back from Tommy John surgery last August. If he makes it back this season, it will be only for a brief stint at the end of the year. The move makes way for the Dodgers to add Danny Duffy, who's making his way back from a forearm injury of his own.