Textile artist and painter Dagmar Olrik was born on June 28, 1860 in Copenhagen, Denmark into a family of liberal arts scholars and artists. Father Henrik Benedictus Olrik was a noted painter and sculptor, passing on his interest in oil painting to his daughter Benedicte; her brothers Axel a folklore historian, Jorgen a museum director, Eyvind a Supreme Counrt Judge, and Hans a historian and educator. At age nineteen Olrik attended the Draftsmanship and Industrial Design School for Women for one year before being tutored by her father and painter Viggo Pedersen. It was around this time that she learned weaving, as well, though it wasn't until 1900 that she began to pursue it as her primary medium.

Her first exhibition took place in 1893 at Charlottenborg, the premier exhibtion hall of Denmark where she would frequently show throughout her career. In 1900 she took a study trip to Europe where she studied under painter Erolo Eroli and learned the art of tapestry weaving and restoration in Florence. On her return to Copenhagen in 1902 she was commissioned by the city of Copenhagen to create a series of tapestries for City Hall in honor of Danish artist Lorenz Frølich's 80th birthday, referencing his illustrations of Norse mythology, and later Adam Fabricius' Illustrated History of Denmark for the People (1852). Olrik formed a workshop in which she directed the design and execution of the pieces. The project would take 18 years to complete, in which time she trained several weavers and was credited with reviving the art of Danish tapestry weaving.

In addition to her artistic pursuits she was also a tapestry restorer and was hired by the National Museum, Copenhagen University, the Frederiksborg Museum, and private collectors. In 1920 she was awarded the Medal of Merit award for her tapestry work.

Dagmar Olrik died on September 22, 1932, in Klampenborg, Denmark. She is buried in Copenhagen.