Wells Fargo & Co.’s board was accused of breaching its duty to investors in a lawsuit that also names Carrie Tolstedt, the executive whose community banking unit created unauthorized customer accounts to reap extra fees.

The suit adds to the mounting pressure on Wells Fargo and Chief Executive Officer John Stumpf since the bank agreed Sept. 8 to pay $185 million in fines and penalties to resolve regulators’ allegations it created more than 2 million deposit and credit-card accounts without customers’ authorization. Analysts and congressional leaders have called for the bank to claw back Tolstedt’s compensation and for Stumpf to resign.

Board members’ refusal to scale back Tolstedt’s retirement benefits is “a breach of their fiduciary duties to shareholders,” according to the complaint, which may be the first such investor case. The suit, in which Stumpf is a defendant along with Tolstedt and the board, asks a San Francisco state…