Since the beginning of 2024, several countries have been experiencing an outbreak of measles. In the modern-day Internet of Everything lifestyle, social media platforms such as YouTube and TikTok have gained widespread popularity on a global scale due to their ability to facilitate the easy creation and dissemination of videos. During virus outbreaks of the recent past, videos on social media platforms played a crucial role in keeping the global population informed and updated regarding various aspects of the outbreaks. As a result in the last few years, researchers from different disciplines have focused on the development of datasets of videos published on YouTube, TikTok, and similar websites. No prior work in this field has focused on the development of a dataset of videos about the ongoing outbreak of measles, published on social media platforms. The work of this paper aims to address this research gap and presents a dataset that contains the data of 4011 videos about the ongoing outbreak of measles published on 264 websites on the internet between January 1, 2024, and May 31, 2024, available at https://dx.doi.org/10.21227/40s8-xf63 . These websites primarily include YouTube and TikTok, which account for 48.6% and 15.2% of the videos, respectively. The remainder of the websites include Instagram and Facebook as well as the websites of various global and local news organizations. For each of these videos, the URL of the video, title of the post, description of the post, and the date of publication of the video are presented as separate attributes in the dataset. After developing this dataset, sentiment analysis (using VADER), subjectivity analysis (using TextBlob), and fine-grain sentiment analysis (using DistilRoBERTa-base) of the video titles and video descriptions were performed. This included classifying each video title and video description into (i) one of the sentiment classes i.e. positive, negative, or neutral, (ii) one of the subjectivity classes i.e. highly opinionated, neutral opinionated, or least opinionated, and (iii) one of the fine-grain sentiment classes i.e. fear, surprise, joy, sadness, anger, disgust, or neutral. These results are presented as separate attributes in the dataset for the training and testing of machine learning algorithms for performing sentiment analysis or subjectivity analysis in this field as well as for other applications. Finally, this paper also presents a list of open research questions that may be investigated using this dataset.