This paper presents a quantized output feedback model reference adaptive control (MRAC) scheme for a class of single-input and single-output discrete-time linear time-invariant systems with unknown parameters. Our method, firstly, integrates the well-known MRAC and quantized control techniques to construct a quantized output feedback adaptive control law with parameter update laws. Then, some vital technical lemmas are developed, fundamentally applicable to finite and infinite quantized output feedback MRAC. Moreover, we prove that in the case of infinite quantization, appropriately choosing the output quantizer’s sensitivity affords the proposed adaptive control law to ensure closed-loop stability and achieve bounded or asymptotic output tracking. The significant advantage of the developed adaptive control scheme is combining the benefits of the classic MRAC and quantized control. Compared with current adaptive tracking control schemes, the developed scheme not only reduces the feedback information requirement, but also has full capability to achieve closed-loop stability and output tracking. The effectiveness of the proposed MRAC scheme is verified through several simulations.