Fischer was born in Fort Wayne, Indiana, United States, and was raised in suburban St. Louis, Missouri. Her mother, Anne (née Miller), is a history teacher, and her father, James E. "Jim" Fischer, is a plastics engineer. Fischer has one younger sister, Emily, a third grade teacher. Fischer first performed at the age of six, when she participated in an acting workshop taught by her mother at Henry School in St. Louis, a workshop also attended by actor Sean Gunn, with whom she grew up.