In this paper, we propose a fast Maximal Empty Rectangle (MER) enumeration algorithm for online task placement on reconfigurable Field-Programmable Gate Arrays (FPGAs). On the assumption that each task utilizes rectangle-shaped resources, the proposed algorithm can manage the free space on FPGAs by an MER list. When assigning or removing a task, a series of MERs are selected and cut into segments according to the task and its assignment location. By processing these segments, the MER list can be updated quickly with low memory consumption. Under the proof of the upper limit of the number of the MERs on the FPGA, we analyze both the time and space complexity of the proposed algorithm. The efficiency of the proposed algorithm is verified by experiments.