MLB announced the suspension and an undisclosed fine for Hinch on Sunday, two days after the incident in the Astros' spring game against the Cardinals.
Hinch will serve the suspension Sunday for Houston's game against Atlanta.
"The fact that he wanted to throw me out in a spring training game is pretty ridiculous," Hinch said after being tossed one pitch into the bottom of the first inning. "He's known for overreaction a little bit."
Hinch's postgame comments angered Hernandez.
"He said that? Write it," Hernandez said before adding, "No comment. He got ejected for arguing balls and strikes. That's it."
Hinch said about a week ago Hernandez admitted to him that he gets about four ball-strike calls wrong per game.
After a few of those calls didn't go Houston's way in the top of the first inning, Hinch said he calmly made a suggestion to Hernandez as the Astros prepared to bat.
"We have technology to help you get better and that these pitches are strikes," Hinch said he told Hernandez. "He had kind of an arrogant attitude about it and didn't want to hear it."
When Hernandez called the first pitch to Astros leadoff hitter George Springer a strike, Hinch said he thought Hernandez probably made the call out of spite.
From the dugout, Hinch said he yelled to Hernandez that he'd used up his allotment of missed calls, prompting the ejection.
Hinch emerged from the dugout and began a lengthy and at times heated conversation with Hernandez at home plate.
"When you argue balls and strikes you get thrown out, I get it," Hinch said. "As it escalated, he said some condescending things that are inappropriate, unprofessional. I'll leave it at that and we'll move on to the next game."
First-base umpire CB Bucknor attempted to intervene, but Hinch wouldn't leave the plate area for more than two minutes. At one point, Hernandez clapped his hands as if to say, "Let's go, argument over."
Hinch mockingly clapped back at him.
"I should thank CB. He was the voice of reason in all of it," Hinch said. "CB was super calm about it, he just wanted the game to continue."
As Hinch grew more agitated, he was restrained by both Springer and coach Alex Cintron. Hinch appeared to bump Hernandez and Bucknor at least once each.
The argument could linger beyond spring training.
"I'm sure we'll revisit this in-season," Hinch said.
Hinch says ump overreacted ejecting him
AJ Hinch reacts to being ejected after one pitch in the bottom of the first inning and says ump Angel Hernandez's ejection was ridiculous.