Barch will miss Thursday night's game in New York against the Rangers.
"Mr. Barch has admitted making the remark, but denies that the comment was racially motivated," senior executive vice president of hockey operations Colin Campbell said in a statement. "While we accept Mr. Barch's assertion, as a player in the National Hockey League, he must be held accountable for making a comment that, in the context in which it was made, and in light of the entirety of the circumstances, was offensive and unacceptable."
Barch was ejected from Florida's win over Montreal Jan. 1. The Miami Herald reported a linesman said he heard an inappropriate comment directed toward Subban, whose parents are Jamaican.
Information from The Associated Press was used in this report.