Rodriguez was at the plate in the eighth inning when Hernandez came up and in with a 88-mph changeup that he couldn't get out of the way of. A-Rod will now head to the disabled list with a non-displaced fracture.
"He's upset," Yankees manager Joe Girardi said. "He wants to be out there. We're not going to have him, and we're going to have to find a way."
Rodriguez was the third batter hit in the game by Hernandez, who also drilled former teammate Ichiro Suzuki in the seventh inning, along with Derek Jeter earlier in the eighth.
Meanwhile, Rangers third baseman Adrian Beltre was hit in the back of the head by a 92-mph fastball by Red Sox reliever Vicente Padilla in the eighth inning. After the Rangers' 2-1 loss, Beltre had a contusion on his head, but he showed no signs or symptoms of a concussion.
"I got hit pretty good," Beltre said. "It's a bruise, but not as bad as it looked."
Beltre's teammate, Ian Kinsler, was hit by a Clay Buchholz pitch in the first inning. He stayed in the game, but was ejected by first-base umpire Tim Tschida after getting picked off.
In the Cardinals' 8-2 win over the Dodgers, the NL was also not immune to hit-by-pitches.
Matt Kemp was hit in the top of the eighth inning by Adam Wainwright. Kemp left after that half-inning, but his exit had nothing to do with the HBP.
Before that, Cardinals first baseman Lance Berkman got drilled on the right knee in the third inning by ace Clayton Kershaw.
While Berkman took the hit off the same spot that he had surgery on just two months ago to repair a torn meniscus, he appears to have avoided something serious enough to land him back on the DL.
"It hurts," said Berkman, who immediately went to the ground after Kershaw's 84-mph slider struck him and was later taken out for a pinch-runner.
"It's a bad bruise in a bad spot, unfortunately. I've already had a lot of trauma to that joint and didn't really need any more. But unfortunately, I got some."