The Islanders also returned Joel Martin to the Sound Tigers.
Haley's recall is on an emergency basis, his second stint with the Islanders. He leads the Sound Tigers in goals (12) and penalty minutes (144).
Montoya was acquired in a trade Wednesday from the Phoenix Coyotes. He has an 11-8-0 record this year with AHL San Antonio.
Martin was recalled Tuesday after Kevin Poulin was injured in pregame warmups. He backed up Mikko Koskinen in both games this week. Koskinen got his first NHL win Thursday night, a 4-3 shootout victory over the Montreal Canadiens.
The last-place Islanders are home Friday night against the Pittsburgh Penguins.