More than 30 firefighters were called to the unit at Bankside Industrial Estate shortly after midnight.
Additional crews from across central Scotland had to be called in due to the "protracted" nature of the blaze.
The Scottish Fire and Rescue Service said the fire was extinguished and made safe by about 05:00.
Two crews were initially sent to the site of the fire before further crews were dispatched due to the severity of the incident.
A total of 35 firefighters were involved in the operation.
A Scottish Fire and Rescue Service spokesman said "Further crews from Denny, Bo'ness, Falkirk and Liberton attended, followed by relief crews from Crewe Toll, Stirling and Alloa due to the protracted nature of the incident."
A fire has broken out at an industrial unit storing tanks of highly flammable acetylene gas in Falkirk.