The 69-year-old leader died due to a cardiac arrest, his family said.
Tur is survived by his wife, son and daughter.
He was elected Member of Parliament in 1985, 1998 and 1999. Tur had, joined Aam Aadmi Party in 2014 and was a close relative of AAP's Punjab convener Sucha Singh Chotepur.
Punjab Chief Minister Parkash Singh Badal and his deputy Sukhbir Singh Badal have condoled the death of Tur.