A foldable razor assembly includes a detachable razor blade embedded at the front end of a handle, a box base with its lateral side pivotally coupled to the rear end of the handle, a cavity defined by the box base and a lid for containing the handle and razor blade, and a box body. Since the handle is pivotally coupled to an end of the box base, the handle can be rotated directly to put the handle and the razor blade into the cavity of the box base, and the lid is turned to cover the cavity when the razor is not in use, so as to reduce the overall storage volume of the razor for an easy storage or carry. The invention can prevent the box body from being separated from the razor or missing, and also can keep the razor from being contaminated by the environment. When it is necessary to use the razor, the lid is opened and the handle is turned to combine with the box body. The invention can be folded or unfolded for easy storage or use.