Turner Sims in Southampton and The Brickworks Museum in Bursledon are among 14 venues in the south east to benefit from the investment, which aims to enhance facilities and improve visitor experiences.
Turner Sims will receive £350,000, while The Brickworks Museum has been awarded £280,000.
The funding forms part of the government’s £1.5 billion Arts Everywhere Fund, which supports cultural projects across England.
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Culture Secretary Lisa Nandy said: “I want everyone, everywhere to feel a sense of pride about where they come from.
“Cultural organisations across the south east are important custodians of local identity and play a key role in the story we tell ourselves as a nation.
“Our Arts Everywhere Fund is delivering on our commitment to support cultural assets across the country, increasing access and preserving them for future generations.”
The latest funding round totals £12.6 million for the south east and is administered by Arts Council England on behalf of the Department for Culture, Media and Sport.
It is divided across three schemes: the Creative Foundations Fund (CFF), the Museum Estate and Development Fund (MEND), and the Libraries Improvement Fund (LIF).
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Hazel Edwards, south east area director at Arts Council England, said: “We are proud to support this new wave of investment through the Museum Estate and Development Fund, the Libraries Improvement Fund, and the Creative Foundations Fund.
“These programmes are strengthening the cultural infrastructure that communities rely on every day, from vibrant local libraries and much‑loved museums to the creative organisations that bring imagination and innovation to our towns and cities.”
Funding will support building improvements, environmental upgrades, and improved accessibility at venues and libraries across the region.
The Brickworks Museum will use its funding for urgent repairs to historic drying sheds.
Future rounds of the funding schemes are expected to open in the coming months.