Already coming off two injury-plagued seasons, Martinez limped away with a strained left hamstring in the fourth inning, after just 57 pitches.
"He said he felt kind of a pop," Mets manager Willie Randolph said.
Martinez, who was not available for comment, will fly back to New York on Wednesday for an MRI exam. He left before the game was over, meaning he didn't see Andino's homer -- which would have made him feel even worse.
Andino had just six extra-base hits and three RBIs in his first 81 major league at-bats, but hit the game-winner 371 feet to left field off Matt Wise (0-1), the sixth Mets pitcher.
"He's got a little juice," Marlins manager Fredi Gonzalez said. "He just got a ball out over the plate. In the major leagues, if you do that to any hitter he'll hit it out. Good for us."
Bad for the Mets, who silently picked at plates of beef, shrimp and rice in the clubhouse afterward.
"As far as Pedro going down, I feel bad for him, obviously," said Mets catcher Brian Schneider, who had three hits. "He's a big part of this team, but what's done is done."
Justin Miller (1-0) allowed one hit in the 10th to get the win for Florida, which had six relievers combine to throw seven innings of three-hit, one-run ball.
Martinez hit Hanley Ramirez on the left elbow to open the game, and Uggla followed with a two-run homer. The lead swelled to 4-0 in the second after Gonzalez hit a leadoff homer and Ramirez's triple to center drove Alfredo Amezaga home easily.
But the real trouble for Martinez arrived without warning in the fourth.
He retired Matt Treanor on a groundout and was clearly in discomfort after the pitch, grabbing both his midsection and lower back region. Randolph and team medical officials rushed to the mound, talked momentarily with Martinez, then shuffled with him back to the dugout.
"We weren't going to mess around," Randolph said.
Martinez, entering the final season of a $53 million, four-year contract, went on the disabled list twice in 2006 with right hip inflammation and a strained right calf. That September, he was diagnosed with a torn rotator cuff, had surgery and didn't pitch in the majors for nearly 11 months.
But he went 3-1 in five starts late last season and was problem-free this spring -- giving the Mets hope that Johan Santana and Martinez would be powerful 1-2 atop their rotation.
Now, that's in question.
"We'll see how it plays out," Randolph said.
Randolph talked at length before the game about how he wasn't going to handle Martinez delicately this season, a much different approach than what New York used last year when the three-time Cy Young Award winner returned for the pennant chase.
That approach almost certainly won't last.
Martinez's best work Tuesday might have come at the plate. He worked a 12-pitch at-bat against Marlins starter Rick VandenHurk in the second, with the crowd getting louder every time the pitcher -- a career .094 hitter entering the night -- fouled one off to the backstop screen.
Martinez eventually struck out swinging to end the inning, but by then, VandenHurk had already thrown 55 pitches.
VandenHurk left after each of the three Mets batters he faced in the fourth all singled, and each of those eventually scored. Pagan's RBI single -- on VandenHurk's 76th and final pitch -- drove in the first run.
"I thought it was a good ballgame," Randolph said.
Andino left the ballpark without comment because of a family matter, the Marlins said. ... It was the 44th time Martinez has allowed at least two home runs in a game, but the first time he ever yielded one in both the first and second innings, according to the Elias Sports Bureau. ... Dominican Republic President Leonel Fernandez threw out the ceremonial first pitch to Ramirez, who, like Martinez, hails from that nation. ... Ramirez is 2-for-12 against Martinez, with a double and a triple.