Millions of people are affected by acute and chronic wounds yearly across the world. Continuous wound monitoring is important for wound specialists to allow more accurate diagnosis and optimization of management protocols. Machine Learning-based classification approaches provide optimal care strategies resulting in more reliable outcomes, cost savings, healing time reduction, and improved patient satisfaction. In this study, we use a deep learning-based method to classify burn wound images into two or three different categories based on the wound conditions. A pre-trained deep convolutional neural network, AlexNet, is fine-tuned using a burn wound image dataset and utilized as the classifier. The classifier's performance is evaluated using classification metrics such as accuracy, precision, and recall as well as confusion matrix. A comparison with previous works that used the same dataset showed that our designed classifier improved the classification accuracy by more than 8%.