The 190-pound White moved his arms and legs and was talking before leaving the field to go to a hospital for examination.
A source told ESPN NFL Insider Adam Schefter that White suffered a concussion.
"The information that we have is that he's doing OK," Dolphins coach Tony Sparano said after the game.
White landed on his stomach following the collision in the third quarter, and Steelers players immediately began waving for help.
"It didn't look good," teammate Chad Henne said. "It was just good to see he was moving."
Air rescue was canceled for White, and he was transported by ground to Broward General Hospital.
Many Dolphins players walked across the field to gather around White as he was treated on the field.
"When I got over there, he was moving around OK," Sparano said.
A group of Steelers players knelt together in prayer.
"It's a scary, scary thing," said Pittsburgh quarterback Ben Roethlisberger, who has had at least four concussions since 2006. "I started to get emotional thinking about it. I went to him and told him to keep his head up and everything will be OK."
The collision came at the end of a 7-yard gain on a keeper by White. Taylor was unhurt.
"I told him, 'I hope you feel better, man,'" Taylor said. "You never want to see a guy down like that. He kept repeating, 'Thanks,' and I just kept telling him to get better."
The game resumed after a delay of 8 minutes.
White took over to begin the third quarter after blurred vision sidelined Henne, the Dolphins' starting quarterback. Henne said he suffered a bruise under his left eye when sacked late in the first half, and his vision became worse at halftime.
"I was hoping it would clear up," he said. "I just didn't have perception. I just couldn't really visualize my throw."
Third-stringer Tyler Thigpen made his first appearance with the Dolphins as a replacement for White and led Miami to two touchdowns, but Pittsburgh won 30-24, and the Dolphins were eliminated from the playoff race.
Information from The Associated Press was used in this report.