Eight crews were sent to the incident at Granville Recycling Plant, Grange Lane, Redhill, Telford, and at its peak there were 50 firefighters battling the blaze.
Shropshire Fire and Rescue Service was alerted at around 4.40am and said the fire was affecting the entire landfill site near the A5.
Group manager Adam Matthews said that the firefighters are now "winning the battle" and the number has been reduced to about 25, but that they will likely still be fighting the fire tomorrow.
He said: "We're making some slow progress now. We've got several main jets in use.
"I would say that we will probably be here all tonight. The smoke plume has died down which is good."
The smoke had been billowing high into the sky above the recycling centre, visible across Telford and from the M54.
Video of the blaze, courtesy of Janice Bannister:
Interactive map of the area:
The site, just up from Telford Naturist Club, used to be run by Telford & Wrekin Council but is now privately owned.
Nearby residents have been warned to keep their doors and windows closed. Visibility on local roads has also been affected however no roads had been closed as of 8am.
Police officers and council workers are also at the scene alongside the firefighters from Albrighton, Bridgnorth, Newport, Shrewsbury, Telford Central, Tweedale and Wellington.
Mr Matthews earlier said that the focus was on dealing with the smoke plume.
He said a national expert in wild fires had been sent to the scene, along with the local crews from across Shropshire.
He said: "There is a large smoke plume obviously coming off this incident and with the current wind direction this plume is heading towards Telford, Priorslee and St George's areas.
"There is no need to panic but as a precaution we would urge people to keep doors and windows closed.
"We are currently working on the scene and have Telford & Wrekin emergency planning and a number of other agencies.
"We are just reviewing our tactical plan and the main thing is to deal with this smoke plume that is heading over Telford."
More to follow.