The scheme will enable Müller to significantly increase yoghurt production and make the Telford plant one of the most technologically advanced dairy production facilities in Europe.
It is also set to see more than 50 new jobs created at the site.
Construction group Kier will build the steel-framed extension to the rear of the existing building on a currently undeveloped section of the site at Donnington Wood.
Preparation work for the expansion has begun but production operations will continue throughout, with the plant remaining operational 24/7. The new facility is due to be operational in early 2019.
Kier Construction Central managing director Mark Pausey said: "Overall, the UK's industrial sector has increased by 1.4 per cent a year since 1948, according to a recent report from the Office for National Statistics (ONS) and this is the latest award for Kier which allows us to build on our expertise in the sector.
"It's an exciting award for the team on such a technically challenging project and using our experience from schemes including the 37,000 m2 units at Kier Park, Frimley and 46,000 m2 at Basingstoke we can ensure the current operations for Müller run without disruption as we work to substantially increase the production capacity."
Last year Müller announced it is to invest £100 million to grow its range of yoghurts and desserts – meaning investment and expansion in its three Shropshire factories.
The company wants to develop new products to let it move into new market areas, while growing sales in those where it is already a significant player.
As part of that the company plans to increase capacity and capabilities at its three Shropshire sites, including the one in Telford.
It also plans to invest in its headquarters at Market Drayton, where Müller makes its own-brand products.
Müller also plans to build on its agreement with Mondelez to develop its range of Cadbury desserts, which are made at its Minsterley factory.