Los Angeles manager Joe Torre said before his team's 10-8 loss to the Oakland Athletics on Monday that Ramirez won't play in exhibition games for at least a week to rest his sore left hamstring.
Torre also said that Schmidt, who made his second start of the spring, is no longer a candidate to begin the season in the rotation because there is not enough time for his rehab from shoulder surgery.
Ramirez aggravated his left hamstring injury while playing the outfield Sunday for the first time this spring. He took batting practice and played catch at the Dodgers' facility Monday, but the club will be cautious about getting him back into a game.
"We're just going to lay low till we get rid of this," Torre said. "We're just going to keep him out. I can't give you a time because I don't know the time, but it's certainly going to be through the weekend and probably beyond that."
The 36-year-old Ramirez played two games after agreeing to a two-year, $45 million deal on March 3. He was the designated hitter once. In his debut in left field on Sunday, he got hurt chasing Troy Tulowitzki's fourth-inning double into the corner.
"A thing we're certainly not going to attempt to do is take a chance with this, and once you start playing it never goes away," Torre said.
Torre said if Ramirez gets "a week or so of at-bats, it should be enough" for him to be ready for opening day.
Meanwhile, Schmidt threw 42 pitches in two scoreless innings against the A's. With three weeks to go before opening day, Torre said there's not enough time to get Schmidt ready to take the No. 5 spot in the rotation.
"This is all about some time down the road, getting him back, but at this point I have no idea when that is," Torre said. "After what he's been through with the surgeries and the whole thing, I think we can look at it as continuing rehabbing."
Schmidt, 36, has not pitched in the majors since June 16, 2007. The three-time All-Star has undergone two shoulder operations since then.
"I'm just trying to get out on the mound," he said. "I'm not looking at opening day or five days from that. I just want to eventually pitch in a game in Los Angeles and pitch in the big leagues. I'm not setting a timetable."
Schmidt left the game with a 4-0 lead, but the A's scored nine runs in the third against Jeff Weaver, Stephen Randolph and Shawn Estes. The pitchers issued four walks and hit two batters as the A's sent 15 hitters to the plate in the inning.
A's starter Trevor Cahill, one of the team's top prospects, was charged with four runs in three innings.
"I felt good, the location just wasn't there," said Cahill, who had allowed only two runs in his first eight innings.
Oakland manager Bob Geren said he was encouraged that Cahill responded from the bad second inning to work a perfect third on 10 pitches.
A's OF Travis Buck had three hits and three RBIs, improving his average to .324 this spring. ... RHP Joey Devine is scheduled to throw off a mound Thursday. It would be his first time on a mound in two weeks. Devine, who has had a sore elbow, is a candidate to close games for the A's. ... 1B Sean Doolittle, who hit .364 with nine RBIs this spring, made an impression on Geren before he was sent to minor league camp on Monday. "He had a great spring," Geren said. "He's a real good, all-around player. He reminds me, just around the bag, of Don Mattingly. He's a smooth fielder. He's a line-drive, gap hitter, but he's shown some power. He has a real bright future." ... LHP Dana Eveland, the leading candidate to get the opening-day start in place of injured RHP Justin Duchscherer, will pitch in a minor league game Wednesday because the A's have an off day. ... A's OF Ben Copeland came out of the game with a sore right shoulder after making a leaping catch against the center-field fence. He was sent to a doctor for evaluation.