According to multiple reports, initial X-rays on the ankle did not reveal a broken bone.
Hernandez will have an MRI on his right ankle Monday, according to a league source. After the game, Hernandez left the stadium with the assistance of crutches, wearing a walking boot on his ankle. It is unclear how long the injury will keep him out.
Patriots coach Bill Belichick did not have an update on Hernandez's status immediately following the game.
Hernandez was tied up while blocking on a screen pass to receiver Julian Edelman early in the first quarter. The star tight end appeared to injure his right ankle when another player fell on him as he went to the ground.
"You can't go into the game just counting on one guy, any guy," Belichick said. "Everybody has to be ready to adjust. It's not the first time a player has been injured in a game."
The injury caused the Patriots to drastically alter their offensive personnel. After using two or more tight ends on all 67 offensive plays in Week 1 against the Tennessee Titans, New England used a pair of tight ends on just 20 of 77 offensive plays Sunday.
Since the start of the 2011 season, the Patriots used two tight ends or more on 80 percent of their offensive plays.
"He's part of the game plan the whole week, obviously," Gronkowski said. "He's a great player. You just gotta be prepared though -- any time, any situation for anything. We gotta be more prepared and be able to go out and do the offense."
Brady said he was uncertain whether Hernandez's absence slowed the Patriots' offense.
"We have an offense with him in the game and without him in the game," Brady said. "Guys go in and out, and you lose guys over the course of a game and you have to be able to adjust.
"I'm sure he's not going to be the only one we lose this year at some point, but we have to figure out a way to still move the ball effectively throughout the course of the game -- enough where we can score more than 18 points."
Without Hernandez, the Patriots went away from their base offense with multiple tight ends, relying more on a three-receiver package.
"When he went down, it took away a lot of things they are able to do," said Cardinals safety James Sanders, who played for the Patriots from 2005-10. "It's unfortunate for them, but it helped us out as a unit. I just pray that he's healthy."
ESPNBoston.com's Mike Rodak and Field Yates contributed to this report.