The detection and analysis of circulating tumor cells (CTCs) may enable a broad range of cancer-related applications, including the identification of acquired drug resistance during treatments. However, the non-scalable fabrication, prolonged sample processing times, and the lack of automation, associated with most of the technologies developed to isolate these rare cells, have impeded their transition into the clinical practice. This work describes a novel membrane-based microfiltration device comprised of a fully automated sample processing unit and a machine-vision-enabled imaging system that allows the efficient isolation and rapid analysis of CTCs from blood. The device performance was characterized using four prostate cancer cell lines, including PC-3, VCaP, DU-145, and LNCaP, obtaining high assay reproducibility and capture efficiencies greater than 93% after processing 7.5 mL blood samples from healthy donors, spiked with 100 cancer cells. Cancer cells remained viable after filtration due to the minimal shear stress exerted over cells during the procedure, while the identification of cancer cells by immunostaining was not affected by the number of non-specific events captured on the membrane. We were also able to identify the androgen receptor (AR) point mutation T878A from 7.5 mL blood samples spiked with 50 LNCaP cells using RT-PCR and Sanger sequencing. Finally, CTCs were detected in 8 of 8 samples from patients diagnosed with metastatic prostate cancer (mean $pm$ SEM = 21 $pm$ 2.957 CTCs/mL, median = 21 CTC/mL), thereby validating the potential clinical utility of the device.