Christian Bergman replaced him.
De La Rosa said he wanted to stay in the game, but understood why the move was made.
"I think it was a smart thing to take me out, "De La Rosa said. "It was bothering me the whole game. That's why they took me out because they don't want it to get worse.
"I told them [I wanted to stay in], but they made a smart decision."
Up until that point, though, De La Rosa was cruising. In five-plus innings, he gave up just three hits, walked one and struck out three. The second of his two walks eventually came around to score, which gave Arizona a 1-0 lead, but Bergman prevented any further damage.
De La Rosa originally suffered the cut during a pregame bullpen session before his May 21 start against the Phillies. He next outing was pushed back twice in order to give his finger more time to heal, and after starting against the Dodgers on June 2, he was again given extra rest before starting on June 9.
Weiss said it's "to be determined" if De La Rosa will miss any additional time.
"We know this is something he's had in the past, and typically, he's been able to get over it," Weiss said. "That cut opened up pretty good. We felt like if we let him go any longer, he was really going to tear that thing and maybe be looking at a possible DL situation. So we wanted to get him out of there at that point.
"But it's something that's been fairly chronic, so there's some concern there."
Dargan Southard is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.