In this paper, we present a delay-optimal packet scheduler for processing the M2M uplink traffic at the M2M application server (AS). Due to the delay-heterogeneity in uplink traffic, we classify it broadly into delay-tolerant and delay-sensitive traffic. We then map the diverse delay requirements of each class to sigmoidal functions of packet delay and formulate a utility-maximization problem that results in a proportionally fair delay-optimal scheduler. We note that solving this optimization problem is equivalent to solving for the optimal fraction of time each class is served with (preemptive) priority such that it maximizes the system utility. Using Monte-Carlo simulations for the queuing process at AS, we verify the correctness of the analytical result for optimal scheduler and show that it outperforms other state-of-the-art packet schedulers such as weighted round robin, max-weight scheduler, fair scheduler and priority scheduling. We also note that at higher traffic arrival rate, the proposed scheduler results in a near-minimal delay variance for the delay-sensitive traffic which is highly desirable. This comes at the expense of somewhat higher delay variance for delay-tolerant traffic which is usually acceptable due to its delay-tolerant nature.