He had 13 goals and 39 assists in 75 games with the Islanders but turned that into a $2.85 million award following Thursday's arbitration hearing.
Snow, the team's backup goalie until he took over for fired GM Neil Smith last week, spent his first day on the job Wednesday trying to avoid arbitration with York.
"We respect the arbitrator's decision and appreciate the process that led to the one-year award for Mike, a player we think the world of," Snow said in a statement. "It was our intention prior to the hearing to sign him to a long-term deal, and it remains our hope to have Mike York in an Islanders uniform for years to come."
The figures submitted by each side were not disclosed, but the Islanders offered York -- a restricted free agent -- a $2.05 million qualifying offer to keep him off the unrestricted market.
York, Snow's teammate last season, instead elected to take the Islanders to arbitration.
Unless a deal is reached in time, Snow and the Islanders face another arbitration hearing next week with forward Arron Asham.
Asham earned $627,000 last season and was given a $689,700 qualifying offer.