Barnsley Council said the closure could be extended depending on the extent of damage or any further vandalism which had delayed repairs last year.
Upcoming work will include the demolition of the damaged roof slab, the fixing of new reinforcement steel and the reinstatement of the carriageway.
Traffic heading towards Doncaster will be diverted onto Barrowfield Road and Lidget Lane.
Traffic heading towards Barnsley will be diverted onto Doncaster Road and Barnsley Road through Goldthorpe town centre.
A spokesperson for Barnsley Council said: “We understand that this closure may raise concerns among local residents and visitors.
“We thank you for your understanding and cooperation during this time.
“Your safety remains our top priority, and we’re committed to resolving the situation as swiftly as possible.”
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