The work, which will be completed by Thursday, 10 December subject to weather, will involve the replacement of bridge joints and resurfacing of the bridge deck.
Highways England Area Manager, Julian Strong, said:
We will be working between 7pm and 6am to ensure the work causes the minimum of disruption to drivers.
When complete this work will prolong the life of the carriageway and maintain safety on this stretch of the A38.
Overnight closures on the bridge and its approaches will be required in both directions with only one carriageway closed at any time, A clearly signed diversion route will be in place.
Southbound traffic will be directed on to the old A38 through South Brent via the B3372 (Marley Head to Wrangaton). Northbound traffic will follow the same route in reverse.
Members of the public should contact the Highways England customer contact centre on 0300 123 5000.
Journalists should contact the Highways England press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.