Ethier received a pain-killing epidural injection, but he cannot perform any baseball-related activities for a week to 10 days.
Dodgers manager Dave Roberts told the Los Angeles Times it would be "tough" for Ethier to be ready by April 3.
Ethier has dealt with soreness in his back and hip for much of March, and he was unable to get it loose for Sunday's game.
Roberts said the injection alleviated some of the pain, but the team is not rushing to get Ethier back by the opener.
"We're just not trying to put so much emphasis on that," Roberts said, according to the Los Angeles Times. "And Andre understands that too. The No. 1 thing is we've got to get him back healthy and feeling good.
"So whenever that day is, whether it's prior to Opening Day or it's not, that's our goal."
Ethier sustained a broken right leg last March, and that limited him to 16 games last season, when he hit .208 with one home run.
Andrew Toles was fighting to earn a spot on the Dodgers roster this spring, but now he might be the team's starting left fielder on Opening Day.