New York (6-7) set a season best with 13 hits in Monday's 7-3 victory, as Lucas Duda went 4 for 5 with a pair of RBIs. David Wright drove in two runs and extended his hitting streak to six.
Lagares, the Mets' leading hitter with a .314 average, doubled to give him a nine-game hitting streak, but he left in the seventh inning with a strained right hamstring suffered while running out a grounder.
Granderson left in the sixth with rib and forearm pain after running into the wall in the first. X-rays came up negative, but he's expected to be out a few days.
Lagares, though, could miss much more time.
"It's really tough," manager Terry Collins said. "(Lagares has) played absolutely great (and) he's earned that right to be out there every day. For this to happen to him now, it's a tough break for him and a tough break for everybody.''
The Mets hope their pitching can help make up for the losses in their lineup, but they entered this series with a 4.97 ERA while ranking last in the majors with 21 home runs allowed.
New York got 6 1-3 solid innings from Zach Wheeler on Monday, and Jenrry Mejia will take the mound in this contest looking to improve his command after struggling with it over his first two starts.
Mejia (1-0, 4.09 ERA) allowed one run and struck out eight in six innings of a 4-3 win over Cincinnati on April 4 to overcome five walks, but he walked four while giving up four runs in five frames before the Mets rallied for a 6-4 win at Atlanta on Thursday.
The right-hander threw 101 pitches in his first outing and 98 against the Braves.
"Even when you look at as well as he pitched last year at times, he's going to throw 80-90 pitches in five to six innings," Collins said.
Mejia has never faced the Diamondbacks, whose 5.96 ERA is the worst in the majors.
Bronson Arroyo gave up three runs and six hits - including a pair of homers - in five innings of Wednesday's 6-3 win over the Giants, and he'll oppose Mejia in this contest.
It marked another short outing for Arroyo (1-0, 4.82), who also allowed two runs and five hits in 4 1-3 innings of Arizona's loss to San Francisco on April 3.
The right-hander dealt with a bulging disk that limited his action in spring training, and he said he's still catching up.
"I'm just not quite as strong as I'd like to be," Arroyo said. "Getting up there around 90 pitches, I'm just a bit fatigued. Hopefully I can turn the corner here soon and give this team 105-110 pitches and get into the seventh inning."
Arroyo has tossed three complete games in 14 career starts against New York, pitching at least seven innings 10 times. He's 8-3 with a 3.63 ERA against the Mets, though he hasn't faced them since June 15, 2012.
Another solid outing would be a big help for Arizona (4-12), which is in the midst of its second four-game skid of the young season and has lost six in a row at home.
''We're just not in sync,'' manager Kirk Gibson said.
Miguel Montero went 3 for 3 and drove in all three runs Monday, and he's hitting .444 during a five-game hitting streak.