This cash boost will help museums to conduct maintenance work to improve their facilities for the benefit of visitors, staff, and their collections.
The Department for Digital, Culture, Media and Sport is contributing the extra funding for the second round of the Museum Estate and Development Fund.
Mr Jones said: “We are particularly blessed in our area to have a number of fantastic museums showcasing our heritage.
"They are a key part of what makes our area attractive to tourists and enables local residents to have a richer understanding of our local heritage.
“The Government’s extra £16.9 million in funding from the Museum Estate and Development Fund will protect and widen access to the historic collections in our museums and galleries.
"I urge museums and cultural venues across Harrogate district to submit an expression of interest through the Arts Council website by the deadline of 17 June.”
Museums can enter round two from now and bid for grants of between £50,000 and £5 million. 31 museums across England were supported by the fund in its first round.
Museums and galleries benefitting from the fund’s investments have improved access for communities to their local history.
Funding awarded has helped to complete structural work, prevent flooding, and increase public access, so that more people can visit their collections and enjoy our national heritage.