The dramatic increase in the use of social media platforms for information sharing has also fueled a steep growth in online abuse. A simple yet effective way of abusing individuals or communities is by creating memes, which often integrate an image with a short piece of text layered on top of it. Such harmful elements are in rampant use and are a threat to online safety. Hence it is necessary to develop efficient models to detect and flag abusive memes. The problem becomes more challenging in a low-resource setting (e.g., Bengali memes, i.e., images with Bengali text embedded on it) because of the absence of benchmark datasets on which AI models could be trained. In this paper we bridge this gap by building a Bengali meme dataset. To setup an effective benchmark we implement several baseline models for classifying abusive memes using this dataset. We observe that multimodal models that use both textual and visual information outperform unimodal models. Our best-performing model achieves a macro F1 score of 70.51. Finally, we perform a qualitative error analysis of the misclassified memes of the best-performing text-based, image-based and multimodal models.