Objective. Fetal arrhythmias are a life-threatening disorder occurring in up to 2% of pregnancies. If identified, many fetal arrhythmias can be effectively treated using anti-arrhythmic therapies. In this paper, we present a novel method of detecting fetal arrhythmias in short length non-invasive fetal electrocardiography (NI-FECG) recordings. Approach. Our method consists of extracting a fetal heart rate time series from each NI-FECG recording and computing an entropy profile using a data-driven range of the entropy tolerance parameter r. To validate our approach, we apply our entropy profiling method to a large clinical data set of 318 NI-FECG recordings. Main Results. We demonstrate that our method (TotalSampEn) provides strong performance for classifying arrhythmic fetuses (AUC of 0.83) and outperforms entropy measures such as SampEn (AUC of 0.68) and FuzzyEn (AUC of 0.72). We also find that NI-FECG recordings incorrectly classified using the investigated entropy measures have significantly lower signal quality, and that excluding recordings of low signal quality (13.5% of recordings) increases the classification performance of TotalSampEn (AUC of 0.90). Significance. The superior performance of our approach enables automated detection of fetal arrhythmias and warrants further investigation in a prospective clinical trial.