Wright was escorted off the field by trainer Ray Ramirez while appearing to limp slightly after delivering a 12th-inning single. He was replaced by Mike Hessman.
The Mets beat the Houston Astros 3-2 in 14 innings.
"Something came on about the fourth or fifth inning," Wright said. "I felt real nauseous and just throwing up a lot. I just didn't feel like I was helping out all that much. I felt like I did what I could and then really couldn't do much more after that."
Wright indicated he did not feel any better following the game, but he hoped to return to the lineup for Thursday's series finale.
"Hopefully I'll get some medicine in me and get some fluids in me and try to go tomorrow," Wright said. "But I feel about the same now that I felt during the game. So hopefully that gets better."
Wright, who generally fights any attempts to leave games or to be out of the starting lineup, added that remaining in Wednesday's game was not an option.
"It was just the fact that I just didn't think I could play. Or, if I could play, I couldn't do anything to help those guys out there," he said. "I felt good up until about the fourth or fifth inning, and then something just hit me. I don't know if it's something going through me or I'm just coming down with something. I felt nauseous and dizzy, and more importantly just really throwing up and feeling bad out there. I talked with [manager] Jerry [Manuel] and those guys and they wanted to get someone in there that probably could help them more than I could at that point."
Manuel said he did not notice Wright appearing to limp. The manager added that catcher Josh Thole was feeling similarly ill.
"It's nothing as far as a pulled muscle or anything like that," Manuel said about Wright. "He just was really lightheaded and queasy."
Adam Rubin covers the Mets for ESPNNewYork.com.