Trains have been running at a reduced speed over the bridge on Blunts Hall Road, Witham, since the damage was spotted on Sunday.
The repairs will also have a knock-on effect for road users, who are having to follow a four-mile diversion route.
Network Rail said further repairs to the brickwork were "urgently required".
Ballast that supports the line was being replaced at the weekend as part of a Â£170m upgrade of the mainline.
Network Rail said procedures were not followed and there was a build up of rock on one side of the bridge, that put too much pressure on it.
A letter to residents said: "J Murphy and Sons Ltd, working on behalf of Network Rail, will be undertaking this essential repair work to the railway bridge.
"The works will be continuous and require the road to be closed until 7 August 2015."
Network Rail told BBC Essex that the road under the bridge would be open "as soon as possible, and that could be next week".
Work to repair a crumbling bridge which is affecting mainline train services between Norwich and London is expected to last a month, Network Rail has said.