The COVID-19 pandemic has collapsed the public healthcare systems, along with severely damaging the economy of the world. The SARS-CoV-2 virus also known as the coronavirus, led to community spread, causing the death of more than a million people worldwide. The primary reason for the uncontrolled spread of the virus is the lack of provision for population-wise screening. The apparatus for RT-PCR based COVID-19 detection is scarce and the testing process takes 6–9 h. The test is also not satisfactorily sensitive (71% sensitive only). Hence, Computer-Aided Detection techniques based on deep learning methods can be used in such a scenario using other modalities like chest CT-scan images for more accurate and sensitive screening. In this paper, we propose a method that uses a Sugeno fuzzy integral ensemble of four pre-trained deep learning models, namely, VGG-11, GoogLeNet, SqueezeNet v1.1 and Wide ResNet-50-2, for classification of chest CT-scan images into COVID and Non-COVID categories. The proposed framework has been tested on a publicly available dataset for evaluation and it achieves 98.93% accuracy and 98.93% sensitivity on the same. The model outperforms state-of-the-art methods on the same dataset and proves to be a reliable COVID-19 detector. The relevant source codes for the proposed approach can be found at: https://github.com/Rohit-Kundu/Fuzzy-Integral-Covid-Detection.