Public Library Innovation Space Act This bill requires the Institute of Museum and Library Services 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 tribal 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) 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 in an amount determined appropriate by the institute. 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.