The motorway was closed during the work which took place between Saturday night and Sunday morning.
The demolished 42-year-old reinforced concrete bridge, which was used to carry farm vehicles between Knowle Park Farm and a field on the opposite side of the motorway, was 43 metres long and weighed around 600 tonnes.
It was knocked down as it was not wide enough to get the extra motorway lane or the lengthened slip roads underneath, so will be replaced with a bridge with wider spans.
Over the following months new bridge supports will be put in place and a replacement deck lifted into position. This will require a further closure of the M1 between the same junctions at a later date. The new bridge will have two spans with a combined length of 67 metres.
The contract to widen a 14-mile (23 km) section of M1 between Junction 25 at Sandiacre and Junction 28 at Pinxton was awarded to Anglo-French joint venture MVM in January 2007. The consortium consists of Morgan-Est, VINCI Construction Grands Projets and Sir Robert McAlpine. The scheme designers are Gifford-WSP. Work started on 29 October and is expected to take three years. The demolition contractor was Armac Demolition and traffic management was carried out by Moxon Traffic Management.