The presence of perineural invasion (PNI) by carcinoma in prostate biopsies has been shown to be associated with poor prognosis. The assessment and quantification of PNI are, however, labor intensive. To aid pathologists in this task, we developed an artificial intelligence (AI) algorithm based on deep neural networks. We collected, digitized, and pixel-wise annotated the PNI findings in each of the approximately 80,000 biopsy cores from the 7406 men who underwent biopsy in a screening trial between 2012 and 2014. In total, 485 biopsy cores showed PNI. We also digitized more than 10% (n = 8318) of the PNI negative biopsy cores. Digitized biopsies from a random selection of 80% of the men were used to build the AI algorithm, while 20% were used to evaluate its performance. For detecting PNI in prostate biopsy cores, the AI had an estimated area under the receiver operating characteristics curve of 0.98 (95% CI 0.97-0.99) based on 106 PNI positive cores and 1652 PNI negative cores in the independent test set. For a pre-specified operating point, this translates to sensitivity of 0.87 and specificity of 0.97. The corresponding positive and negative predictive values were 0.67 and 0.99, respectively. The concordance of the AI with pathologists, measured by mean pairwise Cohen's kappa (0.74), was comparable to inter-pathologist concordance (0.68 to 0.75). The proposed algorithm detects PNI in prostate biopsies with acceptable performance. This could aid pathologists by reducing the number of biopsies that need to be assessed for PNI and by highlighting regions of diagnostic interest.