This paper shows a method for achieving multi-contact motion for a humanoid robot on a movable object, such as climbing of a stepladder. Recent research has developed methods for achieving multi-contact motion that considers various constraints, such as joint limits, torques, balance constraints, reachability, and collision avoidance. In addition to these constraints, Motion On a Movable Object (MOMO) has the following features: it has to consider an object's balance during the changing of contact points; and it has to handle scenarios where the mass properties of an object are unknown. In this paper, in order to achieve a humanoid robot having MOMO, we propose balance constraints that consider the constraints imposed by an object as well as an online estimation of object's constraints. First, we use object-environment constraints as the robot's constraints, and then we show a method for estimating them based on information provided by the robot's sensors. Next, we show a method for applying the balance constraints to a humanoid motion planner and for executing planned motion with real-time sensor feedback controller. Finally, we evaluate our proposed method through experiments in which a life-sized humanoid robot climbs stepladders that have unknown mass properties.