The move has been imposed by Labour's regional office and comes after the borough's ruling party saw the Tories pick up nine seats in last week's local elections.
It is understood the decision to impose a mandatory mentoring scheme was signed off following discussions between local and national officials.
It will see mentors from the Local Government Association (LGA) offer guidance to Labour councillors. The Express & Star has been told that anyone who refuses to comply with the scheme has been threatened with suspension.
Councillors were also warned they would be suspended if they leaked details of the scheme to the press.
A spokesperson for West Midlands Labour said: "The Labour Party will continue to work with Labour groups and the LGA to ensure that every Labour council is achieving the highest possible standards.
"Sandwell Labour Group, along with all other Labour groups in the region, will therefore receive appropriate support to ensure they continue to deliver high quality outcomes for local residents."
It comes after it emerged a potential challenge to Councillor Maria Crompton's leadership could take place at the Labour group's AGM next week.
Liam Preece had been considered a possible candidate for leader, but he is no longer a councillor after losing his Charlemont with Grove Vale seat to the Tories last week.
Possible alternatives are believed to include Blackheath councillor Kerrie Carmichael, and Bristnall councillor Rajbir Singh.
The AGM itself has been mired in controversy over the decision for it to take place virtually.
Some councillors have privately expressed concerns that the situation could open up the possibility of vote rigging due to a lack of supervision.
It follows chaotic scenes in 2016 when Steve Eling become leader following a re-run election, after a number of his opponent's supporters were barred from voting for administrative reasons.
The lead up to last week's election was dominated by rows overs candidate selections and claims of national party interference in local matters.
And a series of high profile councillors quit Labour, including former leader Yvonne Davies who now sits as an independent.
Labour currently has 58 seats on the council having held all 72 seats in 2019.