A flexible microporous polymer paper (MPP) is prepared with the polymer tubes obtained from the Sonogashira coupling reaction of 1,4‐diiodotetrafluorobenzene and 1,3,5‐triethynylbenzene. MPP has an interconnected network structure of polymer tubes and shows a hierarchical pore structure. Relatively large pores are formed among entangled polymer tubes, while micro‐ and mesopores are generated in the tube walls. MPP is foldable, mechanically stable, and stretchable. When the folding stress is removed, a wrinkle forms along the folded line, as observed in common papers composed of cellulose pulps. The mechanical stability of MPP results from electrostatic interactions between electron deficient tetrafluorobenzene units and electron rich triethynylbenzene units in the polymer. The tensile stress–tensile strain curve shows that MPP can elongate up to 15% strain. MPP is superhydrophobic, showing a water contact angle of 162° and can be used for the filtration of small molecules such as a dye and iodine.