A neural network based flexible object manipulation system for a humanoid robot on FPGA is proposed. Although the manipulations of flexible objects using robots attract ever increasing attention since these tasks are the basic and essential activities in our daily life, it has been put into practice only recently with the help of deep neural networks. However such systems have relied on GPU accelerators, which cannot be implemented into the space limited robotic body. Although field programmable gate arrays (FPGAs) are known to be energy efficient and suitable for embedded systems, the model size should be drastically reduced since FPGAs have limited on-chip memory. To this end, we propose ``partially'' binarized deep convolutional auto-encoder technique, where only an encoder part is binarized to compress model size without degrading the inference accuracy. The model implemented on Xilinx ZCU102 achieves 41.1 frames per second with a power consumption of 3.1W, {\awano{which corresponds to 10x and 3.7x improvements from the systems implemented on Core i7 6700K and RTX 2080 Ti, respectively.