She has performed at venues all over the world. Masse, who grew up in rural Maine, is perhaps best known as a member of the charting folk group the Wailin' Jennys.

As a performer, she is a noted soloist as well as a collaborator. She has been a frequent guest on Garrison Keillor's A Prairie Home Companion, in both capacities. On these programs, she has collaborated with a variety of artists including Elvis Costello, Wynton Marsalis, Sheryl Crow, Renee Fleming, and Emmylou Harris. Masse is also celebrated for her performances with contemporary bluegrass band the Wayfaring Strangers and Mark O'Connor's Hot Swing. In 2006, she recorded an album with Joy Kills Sorrow, a contemporary string band. She also led the Brooklyn-based collective Heather & the Barbarians for the album Tell Me Tonight.

In 2008, Masse released her solo debut EP, Many Moons, a collection of jazz-inspired folk duets with pianist Jed Wilson. Her full-length album Bird Song was issued by Red House Records the following year. In early 2011, the Wailin' Jennys released Bright Morning Stars; it won Canadian Juno Award in 2013. That same year saw the release of Lock My Heart, an album of jazz standards and originals recorded in collaboration with pianist Dick Hyman that had a long run on the jazz charts.

Masse, who lives in New York's Catskills region, met jazz trombonist Roswell Rudd during a Prairie Home Companion performance. The pair discovered they were neighbors. Rudd invited her to sing on his Trombone for Lovers album issued by Sunnyside in 2014. They proved natural collaborators. In 2015, during Rudd's 80th year, they began to work on a recording project that combined standards and originals. They were aided by bassist Mark Helias and guitarist Ralf Sturn. The finished album, August Love Song, co-credited to Masse and Rudd, was released by Red House in the winter of 2016. ~ Thom Jurek