Beekeeping is one of the widespread and traditional fields in agriculture, where Internet of Things (IoT)-based solutions and machine learning approaches can ease and improve beehive management significantly. A particularly important activity is bee swarming. A beehive monitoring system can be applied for digital farming to alert the user via a service about the beginning of swarming, which requires a response. An IoT-based bee activity acoustic classification system is proposed in this paper. The audio data needed for acoustic training was collected from the Open Source Beehives Project. The input audio signal was converted into feature vectors, using the Mel-Frequency Cepstral Coefficients (with cepstral mean normalization) and Linear Predictive Coding. The influence of the acoustic background noise and denoising procedure was evaluated in an additional step. Different Hidden Markov Models' and Gaussian Mixture Models' topologies were developed for acoustic modeling, with the objective being to determine the most suitable one for the proposed IoT-based solution. The evaluation was carried out with a separate test set, in order to successfully classify sound between the normal and swarming conditions in a beehive. The evaluation results showed that good acoustic classification performance can be achieved with the proposed system.