Emergency services were called to the blaze at Amcor Flexibles at Brucefield Industrial Estate just before 1200 BST.
One person was taken to St Johns hospital in Livingston where they are being treated for superficial wounds.
Earlier, residents were warned to stay indoors and keep their doors and windows closed because of fears over possible toxic fumes from chemicals.
Lothian and Borders Fire and Rescue Service said the flames were eventually extinguished at about 1800 BST.
At its peak, the fire created a huge plume of black smoke which could be seen for miles.
Local resident Ann Mackay, 51, said: "I saw black smoke all the way from my home in Dedridge, a few miles away, and went to see what was happening.
"I saw the front of the factory building and the sign was melting, but the police asked us to move back as they were evacuating the area."
Neighbouring businesses on the Brucefield Industrial estate were also evacuated.
Local train services between Kirknewton and Shotts were suspended as a precaution until further notice.
Trains are running from Glasgow to Shotts, and from Kirknewton to Edinburgh. The main Edinburgh to Glasgow line is unaffected.
A printing factory fire in West Calder, which involved 70 firefighters and 12 appliances, has been extinguished.