Excessive stress during pregnancy could cause adverse effects for the mother and her unborn baby, disrupting the normal maternal adaptation throughout pregnancy. Such conditions could be tackled to some degree via traditional clinical techniques, although an automated healthcare system is required for providing a continuous stress management system. Internet of Things (IoT) systems are promising alternatives for such real-time stress monitoring. In conventional IoT-based stress monitoring, stress-related data is collected, and the stress level is determined using a pre-defined model. However, these systems are insufficient for pregnant women whose physiological data are changing over the course of their pregnancy. Therefore, an adaptive monitoring system is needed to estimate stress levels, considering the maternal adaptation such as heart rate elevation in pregnancy. In this paper, we propose a stress-level estimation algorithm based on heart rate and heart rate variations during pregnancy. The algorithm is distributed in an edge-enabled IoT system. We test the performance of our algorithm using supervised and unsupervised learning via an unlabelled set of data from a 7-month monitoring. The monitoring was fulfilled for 20 pregnant women using wearable smart wristbands. Our results show a 97.9% accuracy with 10-fold cross validation using Random Forests.