A ceremony was held last Thursday to mark the 'topping out' of the building thanks to almost £1million in grant funding from the Heritage Lottery Fund which will see it double in size.
Lord Lieutenant of Leicestershire, Jennifer the Lady Gretton,
was delighted to mark the occasion by burying a time capsule in the extension.
At the event, she said: "I am delighted to be here today, especially on home territory. This is a wonderful example of public and private sector working together. The finished museum will make a tremendous difference to Melton and I am looking forward to visiting the museum when it is full of all the wonderful exhibits."
The time capsule contains contemporary items selected by staff, volunteers and visitors and included the Melton Times, pictures of the town, plus objects which could become obsolete, from a mobile phone to stamps and a cheque book.
It is hoped the museum, in Thorpe End, will partly reopen in October before fully opening in spring 2010.
The new space will include a community archive to support local history groups, the Museum of Hunting Trust, family history research and more.
And a large section will focus on contemporary rural life, looking at issues affecting the villages in the borough and their relationship with Melton.
Jenny Dancey, keeper of Melton Carnegie Museum, said: "We will use the community archive to engage people interested in local history. We have three ongoing projects and the results of that work will go in the new museum. We hope that's something that will continue to thrive and grow."