Public Library Innovation Space Act This bill requires the National Museum and Library Services Board to carry out a program for making competitive grants to eligible partnerships (composed of a public library and an economic development corporation, a local government, a state government, an elementary or secondary school, a museum, an institution of higher education, a nonprofit organization, a corporation, and/or other entities identified by the Board) to establish makerspaces at public libraries. A makerspace is a facility (which may be at a fixed location or a mobile unit) that is open to the public and provides individuals with access to: (1) tools, technology, and educational resources designed to enable such individuals to create physical goods, including prototypes; and (2) educational opportunities, including vocational training and assistance with early-stage business ventures. A partnership must contribute, for the activities for which the grant was awarded, nonfederal matching funds equal to the grant amount. Each eligible partnership that receives a grant may not use its grant funds, or the matching funds contributed by it, for construction activities at a public library that would provide extra square footage to house a makerspace.