A membrane separation device and a membrane separation method, where membrane clogging is less probable to occur, membrane separation can be conducted even when water to be processed has a relatively slower flow speed, membrane filling efficiency is excellent, and foreign objects are less likely to accumulate in the device. The device has vessel-like inner casings in series in a pressure container having an inlet for water to be treated at one end and a concentration water outlet at the other end. Flow straightening plates are placed on the side of the inlet for water to be processed of the pressure container, a large number of membrane separation elements are stacked in each inner casing, and spacers that serve also as seal members are placed between adjacent membrane separation elements. A through hole is so formed as to penetrate through the membrane separation elements including the spacers from one side to the other side of the stacked membrane separation elements. Permeated-water discharge passages are formed in a length direction in each inner casing. The through hole is in communication with the permeated water discharge passages, and water to be processed that is introduced into the pressure container through the flow straightening plate permeates through the membrane separation elements and is discharged to the outside through the through hole and the permeated-water discharge passages.