Kulibaev is married to the second of the president's three daughters, Dinara.
Another son-in-law in the first family, Rakhat Aliev, was recently divorced by the president's eldest daughter, Darigha. He was dismissed from his post as ambassador to Austria in May, and is facing serious criminal charges. Austrian authorities have so far refused Kazakhstan's request for his extradition.
RFE/RL's Kazakh Service says the president was behind today's order to remove Kulibaev from the deputy chairman's seat at Samruk, which oversees government stakes in the energy sector and other key sectors.
Kazakh state media gave no reason for the 40-year-old Kulibaev's dismissal, and offered no hint at any future appointment.
He had served as Samruk's deputy chairman since it was established by presidential decree in January 2006.
Kulibaev is a Moscow-educated economist who previously worked in leading posts at top Kazakh energy companies KazMunaiGas and KazTransOil.
(with material from agency reports)