The game was scheduled for a 5.30 kick-off.
Stenhousemuir said it was because of 'weather-related flooding and structural damage' at Ochilview.
A club statement read: "Today's game against Rangers FC has been called off due to the gale force winds sweeping across the country accompanied by torrential rain.
"The tickets for today's game will remain valid for the re-arranged fixture which has yet to be scheduled."
League One leaders Rangers were looking to record a 21st successive competitive win.
A statement on Rangers' website added: "Discussions about a date for the rearranged game will occur between both clubs and the SPFL in due course."