Banner, who won the job after training camp, was injured in the fourth quarter of the Steelers' 26-16 win against the Giants.
"Everything's going to be OK," he said, thanking everyone for supporting him and reaching out. "I'm going to get over this. I'm excited about my recovery process, and I'm going to come back even stronger next season. It's another obstacle that I've got to get over."
Banner, 26, is scheduled to be an unrestricted free agent after the season.
He didn't specify his injury, but the NFL Network reported that the initial diagnosis was that he'd torn his ACL.
After an offseason in which he dropped weight, ate healthier and went on a training camp social media hiatus, Banner won the starting job over Chuks Okorafor.
"It can be a cold game, but it's a lot like life," coach Mike Tomlin said. "We're not defined by what happens to us. We're defined by how we respond to it. ... We talk openly about that. It's not that he got injured after all he's been through and the fight that he's been through to get where he is. It's about what he does moving forward in response to it.
"He's a competitor. He's a professional. And I expect him to smile in the face of adversity."
Banner is out for the season, but Tomlin is optimistic about the other pair of Steelers -- running back James Conner and guard Stefen Wisniewski -- who were injured during Monday's win against the Giants.
"We're still in the process of getting scans on [Wisniewski] and James Conner," Tomlin said. "But I think their forecast is a more favorable one, so we'll leave the light on for those two."
Although Conner was feared to have sprained his ankle early in the game, he avoided a high-ankle sprain, a source told ESPN's Jeremy Fowler, adding that the third-year back is expected to get more clarity this week.
The Steelers are waiting on further tests on Wisniewski, who exited one play before Banner's injury because of a pectoral injury.
The Steelers' line is already in a tenuous position because Wisniewski was a replacement for injured veteran David DeCastro, who has been out for more than two weeks because of a knee injury aggravated in a training camp scrimmage.
Rookie Kevin Dotson replaced Wisniewski in the fourth quarter Monday, and Okorafor took over for Banner.