The funding was announced by Member for Albury Greg Aplin.
The LibraryMuseum will receive $135,000 funding over three years, which will be used for exhibitions and programs.
MAMA will receive $40,000 to stage SPEED: faster, larger, stronger, quieter a contemporary exhibition to celebrate the role and presence of motorised transport in regional centres.
MAMA Director Jacqui Hemsley said: "Arts NSW is our premier state funding body and we are thrilled that they value this unique and fully curated exhibition that will be at MAMA in 2016."
Deputy Mayor and chair of the Community and Cultural Committee Cr David Thurley said it was a great example of the State Government and AlburyCity partnering to make Albury a significant cultural destination.
"We welcome this support and look forward to more opportunities to work with the State Government to develop our cultural and creative economy," Cr Thurley said.