Aurora A kinase localizes to centrosomes and is required for centrosome maturation and spindle assembly. Here we describe a microtubule-independent role for Aurora A and centrosomes in nuclear envelope breakdown (NEBD) during the first mitotic division of the C. elegans embryo. Aurora A depletion does not alter the onset or kinetics of chromosome condensation, but dramatically lengthens the interval between the completion of condensation and NEBD. Inhibiting centrosome assembly by other means also lengthens this interval, albeit to a lesser extent than Aurora A depletion. By contrast, centrosomally nucleated microtubules and the nuclear envelope-associated motor dynein are not required for timely NEBD. These results indicate that mitotic centrosomes generate a diffusible factor, which we propose is activated Aurora A, that promotes NEBD. A positive feedback loop, in which an Aurora A-dependent increase in centrosome size promotes Aurora A activation, may temporally couple centrosome maturation to NEBD during mitotic entry.