The Curie temperature of diluted magnetic semiconductor (DMS) nanowires and nanoslabs is investigated using the mean-field model. The Curie temperature in DMS nanowires can be much larger than that in corresponding bulk material due to the density of states of one-dimensional quantum wires, and when only one conduction subband is filled, the Curie temperature is inversely proportional to the carrier density. The TC in DMS nanoslabs is dependent on the carrier density through the number of the occupied subbands. A transverse electric field can change the DMS nanowires from the paramagnet to ferromagnet, or vice versae.