Peverley was later taken to a hospital and the game between the Stars and Columbus Blue Jackets halted.
After Peverley collapsed players from both teams and fans waited in silence.
The Stars and Blue Jackets eventually left the ice entirely.
The 31-year-old from Kingston, Ont., joined Dallas this season and has seven goals and 23 assists in 62 games.
Peverley has 84 goals and 157 assists in 442 NHL games with Dallas, Nashville, Atlanta and Boston.