We study the tunable optomechanically induced absorption (OMIA) with the quantized field in the system, which consists of a driven cavity and a mechanical resonator with a super-conducting charge qubit via Jaynes-Cummings interaction. Such a OMIA can be achieved by controlling the strength of the Jaynes-Cummings interaction. Moreover, our work shows this OMIA for the quantized fields can be robust against cavity decay in somehow. With the combination of optomechanically induced transparency (OMIT), our proposal may have paved a new avenue towards quantum photon router.