Ultrasound imaging has been used to evaluate lung conditions such as pleura effusion and bacterial and viral pneumonia. The lesions caused by pneumonia show different intensity and texture than healthy lung tissue in ultrasound. However, due to the low signal-to-noise ratio and artifacts of the images, tissue lesions can be challenging to identify or be confounded with other pathologies. This paper proposes an approach for tissue classification in ultrasound images. We used the 2D wavelet transform to decompose lung ultrasound images. Then, we used texture features that include first-order statistics and gray-level co-occurrence features, among others, to characterize the images of healthy tissue and pneumonia. We evaluated feature selection and supervised learning techniques for classification. The best results were obtained with the gradient boosting classifier, with 83.3% accuracy in cross-validation and 90% in testing. This study suggests lung ultrasound could be an effective diagnostic technique for pneumonia caused by COVID-19 and other pathogens without exposing the patients to ionizing radiation.