"It's a little sore. A strain, but not a full tear or anything like that," said Capuano, who will have an MRI either Wednesday or Thursday. "I hope the MRI shows it's not a very serious strain."
The Dodgers have lost three games in a row, and four of five since Greinke's injury.
Capuano, who began the year in the bullpen because of the club's excess of starters, didn't have his best stuff in his first start since October. The left-hander allowed four runs in the first inning on five singles and a walk.
"The first inning was tough, I wasn't hitting my spots," Capuano said. "They hit some seeing-eye balls, and they found holes. Nothing went our way in the first inning. And to have this stupid little injury pushes you over the edge."
Capuano retired the side in the second, but appeared to injure his calf covering first base on a grounder to end the inning. He was removed from the game after walking Jesus Guzman on four pitches to open the third.
"He wanted to try to pitch, but it just didn't make any sense," manager Don Mattingly said. "It's really early. I just can't allow a guy that's had Tommy John to go out there and try to pitch on a leg that he can't use for everything. He's not using his whole body. I couldn't do that to a guy."
Matt Guerrier relieved Capuano and went two innings. Josh Wall, recalled from Triple-A Albuquerque on Monday, entered in the fifth and allowed three runs over two frames. Paco Rodriguez and Kenley Jansen combined for two scoreless frames before Brandon League allowed one run in the ninth.
Meanwhile, the Dodgers' offense continued its trend of wasting scoring opportunities.
The Dodgers loaded the bases with one out in the third, but a Mark Ellis sacrifice fly was the only thing to show for it. Matt Kemp struck out swinging to end the threat.
After that, the home team struggled to get anything going against Padres starter Jason Marquis and did not get a runner back on second base until Carl Crawford doubled with two outs in the eighth.
"It was a battle," said Marquis, who is 7-4 with a 2.53 ERA in 17 career appearances against the Dodgers. "My fastball command wasn't where I wanted it, but my slider-split were pretty good. I tried to tell myself [in the third inning] to just try and minimize the damage. We had a 4-0 lead. I just tried to not let it get out of hand."
Juan Uribe and A.J. Ellis had the only other hits off Marquis, both singles.
The Dodgers made solid contact early in the game, but a strong wind blowing in from center field didn't help. Crawford lined a ball into the gap in left-center in the first, but it died on the warning track for an easy out.
"We had some good swings today, unfortunately the wind held up a few of those," said first baseman Adrian Gonzalez. "But we've got to do a better job."
Kemp continued his slow start to the season with an 0-for-3 night, including two strikeouts. The center fielder is hitting .185 (10-for-54) with no homers and four RBIs through 14 games.
"Matt's pressing pretty good. Tonight he seemed really frustrated," Mattingly said. "The game didn't help. It's one of those games that you jump behind early and nothing kind of seems to go your way, and obviously it didn't go good for him."
Mattingly removed Kemp from the game in the top of the seventh in favor of Skip Schumaker. After the game, the manager said he's considering giving a Kemp a day off.
With Capuano's health in question and Greinke sidelined until mid-June, the Dodgers could move Ted Lilly back into the rotation. The left-hander has been pitching in the Minor Leagues on a rehab assignment, and assistant pitching coach Ken Howell said he looked much better in his latest outing on Tuesday.
"At least we're in a position where we do have a guy like Ted, who has been working his way back and getting arm strength as we go," Mattingly said. "We're kind of fortunate that we had an excess of starters."
And with off-days on Thursday and Monday, the Dodgers won't need a fifth starter until April 24. That allows management some time to sort things out.