Frostic was born in Sandusky, Michigan to Sara and Fred Frostic. When she was 8 months old she suffered from an unknown illness which left her with lifelong symptoms similar to cerebral palsy. Despite physical difficulties Frostic showed an early interest and aptitude for art. In June 1924 she graduated from Theodore Roosevelt High School in Wyandotte, where she was known for using a band saw to create event posters for her school. She continued her studies at Eastern Michigan University earning her teacher's certificate and gaining membership in Alpha Sigma Tau sorority. In 1926 she transferred to Western Michigan University and left in 1927 without completing her degree. She continued her artistic endeavors in metal and plastic, while occasionally teaching, but with the war came a lack of metal to work with and she turned to linoleum block carving. Frostic then turned her linoleum block carving into stationery goods and prints which led to her starting her own printing company, Presscraft Papers. In the early 1950s Frostic opened up a shop selling her prints, books, and other items in Frankfort and in 1960 she bought 40 acres (160,000 m2) of land in Benzonia with the intention of moving herself and her shop. On April 26, 1964 her new shop was open for business and she lived there until her death in 2001. The shop is still open.
Western Michigan University named its school of art after her in 2007, after her 13 million dollar bequest to the University in 2001: the Gwen Frostic School of Art. While given as an unrestricted bequest, the funds have primarily been used for scholarships for students, and for the benefit of the arts and creative writing departments in particular, in respect to her lifelong pursuits.