Kardashian and West are seeking unspecified damages from Hurley and his company, Avos Systems Inc.
"Exclusive rights, such as those sold by plaintiffs to publication of video of the event, are particularly valuable," the lawsuit states. "If people violate these rights ... they are of substantially diminished value."
A message sent through MixBit seeking comment from Hurley was not immediately returned.
West proposed to Kardashian on her 33rd birthday; the couple's first child North West was born in June.
The lawsuit was first reported by celebrity website TMZ.