Penner was born on November 6, 1946, in Winnipeg, Manitoba, to Lydia Agathe Penner (née Winters, 1913–2005) and Edward W. Penner. By the age of four, he had begun making up songs while travelling on the bus with his mother. He taught himself how to play the guitar when he was in grade school, and performed in school choirs and pageants. Through his experiences with his sister Susan, who has Down syndrome, he recognized the therapeutic value of music.

Penner received his high school diploma at Kelvin High School, where he took lead roles in the Gilbert and Sullivan operettas. After graduating from the University of Winnipeg with a Bachelor of Arts degree in economics and psychology, he spent time working with mentally and physically challenged children, using music to comfort and entertain. In 1977, he met choreographer and future wife, Odette Graziella Heyn, with whom he started a children’s dance theatre company. Penner accepted an offer to do a recording, which resulted in the album The Cat Came Back, which launched his career and established him as one of Canada’s leading children’s entertainers. Currently, Penner splits his time between Winnipeg and Toronto. He has four children by his first marriage to Odette Heyn. He remarried in 2016, to theatre director Rae Ellen Bodie.

In 1984, he appeared on the children’s television show, The Elephant Show, singing “The Cat Came Back”. In 1991, he was made a Member of the Order of Canada for “using music and song to entertain and educate his young audience”. In 2011, he was made a Member of the Order of Manitoba.