The grant to Wolverhampton Art Gallery will be spent on restoring stonework and repairing the roof and chimneys, as well as measures to improve energy efficiency.
The museum in Lichfield Street is one of 29 across the country to receive a share of almost £25 million to upgrade their buildings through the fourth round of the Museum Estate and Development Fund.
Tamworth Castle will also receive £1.7 million as part of the scheme.
Councillor Chris Burden, cabinet member for city development, said the money would safeguard Wolverhampton Art Gallery for future generations.
“This investment ensures the preservation of our historic building and collections while enhancing sustainability and energy efficiency,” he said.
“These improvements will allow us to continue to deliver free groundbreaking exhibitions, creative activities and cultural events in a welcoming and inspiring space for all our community and city visitors to enjoy.”
Culture Secretary Lisa Nandy, who was in Stratford-upon-Avon to announce a new £270 million Arts Everywhere Fund to help organisations in urgent need of financial support
Miss Nandy said arts and culture were important in helping us understand the world.
“They shape and define society and are enjoyed by people in every part of our country. They are the building blocks of our world-leading creative industries and make a huge contribution towards boosting growth and breaking down barriers to opportunities for young people to learn the creative skills they need to succeed.
“The funding we are announcing today will allow the arts to continue to flourish across Britain, creating good jobs and growth by fixing the foundations in our cultural venues, museums, libraries and heritage institutions.”