Coach Gary Kubiak said after the game that initial X-rays were inconclusive, while Leinart said there's a "pretty good possibility I won't be coming back this season.
"It's pretty disappointing. It's tough to swallow, but we'll just move forward," Leinart said. "Everything that's happened to me, this was a great opportunity. ... It's unfortunate, but I'm not going to give up. It's not my nature. I'll just keep moving forward and figure this thing out one step at a time."
A source told ESPN NFL Insider Adam Schefter that Leinart will have his collarbone checked Monday in Houston and "all indications are it's broken."
Leinart was hit hard by defensive end Jeremy Mincey late in the second quarter, landing on his throwing shoulder. He went to the sideline, headed to the locker room for tests and did not return.
T.J. Yates replaced him and drove the Texans into position for a field goal that put them ahead 20-10 at halftime.
"I feel for Matt. He was playing good," Yates said. "If there's one thing that this team knows how to do, it's deal with adversity. We've taken an injury almost every game of the year and the team has rallied around each other and found a way to win."
Leinart was making his first start in two years after replacing Matt Schaub, who is out for the season with a foot injury.
Leinart completed 10 of 13 passes for 57 yards and a touchdown, a 20-yard pass to Joel Dreessen under heavy pressure.
Information from The Associated Press was used in this report.