Ashe's parents came to the United States from China to pursue PhDs; her father, C.C. Hsiao, taught aerospace engineering at the University of Minnesota, and her mother, Joyce, was a biochemist. She has three younger siblings.
Attending the St. Paul Academy and Summit School in the 1970s, Ashe's interest in the brain began in primary school, where she excelled in math, along with music. She obtained her undergraduate degree at Harvard University in 1975 in chemistry and physics, starting as a sophomore at the age of 17. She went on to earn her PhD in brain and cognitive sciences at MIT in 1981 and her MD from Harvard in 1982. 
Ashe's husband, James is a neurologist; she has three children (two sons and a daughter).