(1) Objective: To design an artificial intelligence system for prostate cancer prediction using the data obtained by shear wave elastography of the prostate, by comparing it with the histopathological exam of the prostate biopsy specimens. (2) Material and methods: We have conducted a prospective study on 356 patients undergoing transrectal ultrasound-guided prostate biopsy, for suspicion of prostate cancer. All patients were examined using bi-dimensional shear wave ultrasonography, which was followed by standard systematic transrectal prostate biopsy. The mean elasticity of each of the twelve systematic biopsy target zones was recorded and compared with the pathological examination results in all patients. The final dataset has included data from 223 patients with confirmed prostate cancer. Three machine learning classification algorithms (logistic regression, a decision tree classifier and a dense neural network) were implemented and their performance in predicting the positive lesions from the elastographic data measurements was assessed. (3) Results: The area under the curve (AUC) results were as follows: for logistic regression—0.88, for decision tree classifier—0.78 and for the dense neural network—0.94. Further use of an upsampling strategy for the training set of the neural network slightly improved its performance. Using an ensemble learning model, which combined the three machine learning models, we have obtained a final accuracy of 98%. (4) Conclusions: Bi-dimensional shear wave elastography could be very useful in predicting prostate cancer lesions, especially when it benefits from the computational power of artificial intelligence and machine learning algorithms.