  Since the structure of space-time at very short distances is believed to get
modified possibly due to noncommutativity effects and as the Dirac Quantization
Condition (DQC), $\mu e = \frac{N}{2}\hbar c$, probes the magnetic field point
singularity, a natural question arises whether the same condition will still
survive. We show that the DQC on a noncommutative space in a model of dynamical
noncommutative quantum mechanics remains the same as in the commutative case to
first order in the noncommutativity parameter $\theta$, leading to the
conjecture that the condition will not alter in higher orders.
