This paper proposes frequency domain precoding vector switching (PVS) transmit diversity for synchronization signals to achieve fast physical cell identity (PCID) detection for the narrowband (NB)-Internet-of-Things (IoT) radio interface. More specifically, we propose localized and distributed frequency domain PVS transmit diversity schemes for the narrowband primary synchronization signal (NPSS) and narrowband secondary synchronization signal (NSSS), and NPSS and NSSS detection methods including a frequency offset estimation method suitable for frequency domain PVS transmit diversity at the receiver in a set of user equipment (UE). We conduct link-level simulations to compare the detection probabilities of NPSS and NSSS, i.e., PCID using the proposed frequency domain PVS transmit diversity schemes, to those using the conventional time domain PVS transmit diversity scheme. The results show that both the distributed and localized frequency domain PVS transmit diversity schemes achieve a PCID detection probability almost identical to that of the time domain PVS transmit diversity scheme when the effect of the frequency offset due to the frequency error of the UE temperature compensated crystal oscillator (TCXO) is not considered. We also show that for a maximum frequency offset of less than approximately 8 kHz, localized PVS transmit diversity achieves almost the same PCID detection probability. It also achieves a higher PCID detection probability than one-antenna transmission although it is degraded compared to the time domain PVS transmit diversity when the maximum frequency offset is greater than approximately 10 kHz.