The bridge over the M20 near Maidstone in Kent was hit by a lorry carrying a digger on Saturday.
A motorcyclist suffered broken ribs and a lorry driver was treated for shock.
The M20 will be closed between junctions 1 and 4 coast-bound and junctions 4 and 2 London-bound from 20:00 BST on Friday until 06:00 Monday.
The collapsed section of the pedestrian bridge, near the village of Addington, was removed from the scene last weekend, and the road was reopened a day later.
Highways England said the remaining structure was being constantly monitored and was structurally sound and safe for traffic to pass underneath with a temporary 50mph speed limit in place.
Chief highway engineer Catherine Brookes said: "We naturally need to remove it under safe controlled conditions this weekend.
"We will use the closures to carry out as much work as possible, including barrier repairs, resurfacing and litter picking.
"We will start planning the replacement in due course."
The coast-bound M26 will also be closed from the M25 junction 5.
Diversions will be in place via the A229 and M2/A2 to join the M25 at junction 2.
Local traffic will be able to use the A20.
Access to the A21 from the anti-clockwise M25 will also be closed with a diversion via junction 4.
The M20 is the main route to the Channel Tunnel and Port of Dover.
A footbridge over a motorway which partially collapsed when it was struck by a lorry will be removed at the weekend.