Martha Abelsen (born 1957) is a Greenlandic politician.
She was born in Nuuk and trained as a kindergarten teacher.
[1] 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.
[2] In October 2011, she was named second deputy mayor for Sermersooq municipality.