The Dodgers said Greinke's injury was mild.
"Obviously, we're always concerned when anything happens to any of our guys," Dodgers manager Don Mattingly said. "But at this point, it's still not a huge issue."
Grienke, the Dodgers' No. 2 starter, was making his first spring start after saying he had "zero interest" making the trip for the Dodgers' two regular-season games in Sydney, Australia, March 22-23 against Arizona.
But now Greinke says he'd like to start a game at Sydney Cricket Ground.
"If we're going to be there, which obviously we are, then, yes, I'd like to pitch over there," he said. "I'm looking forward to flying over there."
Uribe drove in Adrian Gonzalez and connected for a solo shot to left field in the fourth.
Diamondbacks starter Randall Delgado made his first spring appearance. He worked 3 2-3 innings, allowing four hits and one run. He struck out two.
Diamondbacks: Randall Delgado gave up four hits and one run in 3 2-3 innings. He started 19 games last season, his first in Arizona after the Diamondbacks acquired him from Atlanta in a seven-player trade.
"I made good pitches and felt good," Delgado said. "It was good for me to face their big league lineup.
Dodgers: If it had been a regular-season game, Greinke believes he would have continued to pitch. The injury to his right calf, he said, felt more like a cramp than a strain. But, he said, "I know if something's bothering you, they're not going to let you stay in that first day of the spring. If you hurt it, you get fired, probably. No one wants to take the chance."
Dodgers outfielder Carl Crawford was scratched before the game because of a tight quadriceps in his left thigh.
"Just a little tightness," said Crawford, who was not scheduled to play Friday at Camelback Ranch against the Chicago White Sox and will not run until the condition subsides.
Mattingly called the move precautionary. Crawford missed 30 games last year with an injury to his right hamstring.
Dodgers catcher A.J. Ellis was sidelined by the flu. He's expected to be back Friday.
Still no word whether the Dodgers will see Cuban shortstop Erisbel Arruebarrena before they leave Arizona on March 16 for Australia, where they play the Diamondbacks in two games March 22-23 in regular-season games at Sydney.
Arrueberrena, a Cuban defector, was in the Dominican Republic and still trying to acquire a work visa when the Dodgers signed him on Feb. 21 to a five-year, $25-million contract.
"I'm hoping we'll see him in camp before we take off," Mattingly said.
Alex Guerrero got his first hits in a Dodgers uniform Thursday. He had a pair of singles and an RBI in four at-bats as a designated hitter. In his spring debut Wednesday, he went 0 for 2 while playing second base. Guerrero is one of several possibilities at second base. A former Cuban shortstop, he has been trying to make the move to second since he arrived at spring camp with a four-year, $28-million contract that he signed in October.