Already as a child, Tove Ólafsson know that she wants to work with her hands. She is first trained as a sculptor – with studies in both Denmark and Italy – but later continues at the Royal Danish Academy of Fine Arts from 1932–35, where she is taught by Einar Utzon-Frank.

Tove Ólafsson makes her debut in 1934 at the Artists' Autumn Exhibition – same year as she marries the Icelandic sculptor Sigurjón Olafsson – exhibits at Charlottenborg's Spring Exhibition 1935–40 and at Charlottenborg's Autumn Exhibition in 1939. In 1944, she becomes the first female member of the artists' association Kammeraterne and the group's first sculptor.

Over the years, Tove Ólafsson receives a long series of honours, including the Eckersberg Medal in 1948 and the Kai Nielsen Memorial Grant in 1959. Several of her sculptures are in the collection of Danish museums.