An accurate classification of upper limb movements using electroencephalography (EEG) signals is gaining significant importance in recent years due to the prevalence of brain-computer interfaces. The upper limbs in the human body are crucial since different skeletal segments combine to make a range of motion that helps us in our trivial daily tasks. Decoding EEG-based upper limb movements can be of great help to people with spinal cord injury (SCI) or other neuro-muscular diseases such as amyotrophic lateral sclerosis (ALS), primary lateral sclerosis, and periodic paralysis. This can manifest in a loss of sensory and motor function, which could make a person reliant on others to provide care in day-to-day activities. We can detect and classify upper limb movement activities, whether they be executed or imagined using an EEG-based brain-computer interface (BCI). Toward this goal, we focus our attention on decoding movement execution (ME) of the upper limb in this study. For this purpose, we utilize a publicly available EEG dataset that contains EEG signal recordings from fifteen subjects acquired using a 61-channel EEG device. We propose a method to classify four ME classes for different subjects using spectrograms of the EEG data through pre-trained deep learning (DL) models. Our proposed method of using EEG spectrograms for the classification of ME has shown significant results, where the highest average classification accuracy (for four ME classes) obtained is 87.36%, with one subject achieving the best classification accuracy of 97.03%.