He was acquired last July from Boston with forward Tyler Seguin and defenseman Ryan Button for forwards Loui Eriksson, Reilly Smith and Matt Fraser, and defenseman Joe Morrow.
"The first thing (Peverley) asked me was how much time was left in the first period," Ruff said.
The Stars went to the airport after the postponement, and even had a scheduled departure for St. Louis that was earlier than it would have been if the game was played. Dallas is scheduled to play the Blues on Tuesday night.
"He's going to be OK," Ruff said. "The care he's getting and the care going forward is the most important thing."