Martha Abelsen (born 1957) is a Greenlandic politician.
She was born in Nuuk and trained as a kindergarten teacher. She also received management training. Abelsen worked for the KANUKOKA, the association of Greenland municipalities, for 15 years. She began work there as a consultant and, in 1999, became director. Abelsen was elected chairman in 2010. She resigned effective September 1, 2013.[1] In October 2011, she was named second deputy mayor for Sermersooq municipality.[2] In 2014, she was named a representative for Greenland on the Executive Council of the Inuit Circumpolar Council.[3]