Harnessing the abundant availability of spectral resources at millimeter wave (mmWave) frequencies is an attractive solution to meet the escalating data rate demands. Additionally, it has been shown that full-duplex (FD) communication has the potential of doubling the bandwidth efficiency. However, the presence of significant residual self-interference (SI), which is especially more pronounced at mmWave frequencies because of the non-linearities in the hardware components, erodes the full potential of FD in practice. Conventionally, the residual SI is canceled in the baseband using digital processing with the aid of a transmit precoder. In this work, we propose a hybrid beamforming design for FD mmWave communications, where the SI is canceled by the joint design of beamformer weights at the radio-frequency (RF) and the precoder as well as combiner in the baseband. Our proposed design preserves the dimensions of the transmit signal, while suppressing the SI. We demonstrate that our joint design is capable of reducing the SI by upto 30 dB, hence performing similarly to the interference-free FD system while being computationally efficient. Our simulation results show that the proposed design significantly outperforms eigen-beamforming.