Cardiovascular diseases are the most common causes of death around the world. To detect and treat heart-related diseases, continuous blood pressure (BP) monitoring along with many other parameters are required. Several invasive and non-invasive methods have been developed for this purpose. Most existing methods used in hospitals for continuous monitoring of BP are invasive. On the contrary, cuff-based BP monitoring methods, which can predict systolic blood pressure (SBP) and diastolic blood pressure (DBP), cannot be used for continuous monitoring. Several studies attempted to predict BP from non-invasively collectible signals such as photoplethysmograms (PPG) and electrocardiograms (ECG), which can be used for continuous monitoring. In this study, we explored the applicability of autoencoders in predicting BP from PPG and ECG signals. The investigation was carried out on 12,000 instances of 942 patients of the MIMIC-II dataset, and it was found that a very shallow, one-dimensional autoencoder can extract the relevant features to predict the SBP and DBP with state-of-the-art performance on a very large dataset. An independent test set from a portion of the MIMIC-II dataset provided a mean absolute error (MAE) of 2.333 and 0.713 for SBP and DBP, respectively. On an external dataset of 40 subjects, the model trained on the MIMIC-II dataset provided an MAE of 2.728 and 1.166 for SBP and DBP, respectively. For both the cases, the results met British Hypertension Society (BHS) Grade A and surpassed the studies from the current literature.