A delegation from Treasury and Public Enterprises met with banks to ask for their help in fixing embattled SOEs.
"We are confident that she will continue serving the country and our movement in other capacities in future."
The Democratic Alliance says it was "vindicated" and that Brown's "time has finally come to face the music".
The ruling comes after trade union Solidarity approached the high court to declare Molefe's controversial award of more than R30-million unlawful.
BLSA CEO Bonang Mohale said Brown did not understand Eskom's role in the economy.
The public enterprises minister is denying allegations against her in Parliament's state capture inquiry.
Explosive allegations have been made against the four at a parliamentary inquiry.
Lynne Brown says that the new Eskom board members will be vetted, but she cannot tell who their friends are.