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.

Lance Corporal Mapp, of the Household Cavalry, finished 0.18 seconds ahead of American Jason Storm in Igls, Austria.
"What a feeling," said Mapp. "Delighted to win the first Para bobsleigh gold."
Mapp lost both legs when his military vehicle ran over an explosive device in Afghanistan in 2010. He is in the GB sitting volleyball team and took part in the Invictus Games.
He said: "Being part of the world's first ever Para bobsleigh race today was incredible. To win was something really special.
"I hope that I have done people proud - I've had so much support from many different people.
"Help for Heroes have been instrumental in supporting me to this point - it's been great to have their backing.
"I love bobsleigh. I only tried it for the first time in Calgary last season so to be here in Austria, at the first ever race and win is just amazing.
"I feel so excited about where the sport is going and for our next race in St. Moritz next week.
"The field of athletes has been strong and there's been some tough competition. It was an amazingly close race - only three-tenths of a second between the top four finishers.
"To think I nearly quit bobsleigh last summer to focus on my other sports. It's been a fantastic experience to be here, with such a great group of competitors. "
Para bobsleigh and Para skeleton are being included at World Cup events for the first time this season but the International Paralympic Committee have said that the sports will not be included in a Winter Paralympics until 2022 at the earliest.

Chris Sane left South Gloucestershire Council days before it emerged the cost of building the North Fringe to Hengrove route had risen £4.6m since November.
Amid months of traffic delays, the construction bill is now £16m higher than forecast two years ago.
Mr Sane resigned on 30 June for "personal reasons", the council said.
"We can confirm that Chris Sane has now left South Gloucestershire Council, with effect from 30 June," a spokeswoman said.
"Alternative arrangements have been put in place to cover this role in the interim."
Earlier this week, a report to the council's cabinet authored by the now former head of transport revealed construction delays were behind the rising costs of the MetroBus route, which runs from Cribbs Causeway to the north of Bristol, through the city centre to Hengrove in south Bristol.
South Gloucestershire will need to spend an extra £9.8m above its original £30.5m contribution to the scheme to cover the increased costs.
The report recommended the extra cash is taken from the highways maintenance budget over the next 10 years.
Commuters have been enduring roadworks associated with the scheme in the city centre, on the M32 and various other locations in South Gloucestershire.
A footbridge over a motorway which partially collapsed when it was struck by a lorry will be removed at the weekend.
[NEXT_CONCEPT]
Great Britain's Corie Mapp won gold in the inaugural World Cup Para bobsleigh race.
[NEXT_CONCEPT]
The man in charge of delivering a major part of Bristol's MetroBus network has resigned from his role.