Early detection and accurate diagnosis can predict the risk of malignant disease transformation, thereby increasing the probability of effective treatment. A mild syndrome with small infected regions is an ominous warning and is foremost in the early diagnosis of diseases. Deep learning algorithms, such as convolutional neural networks (CNNs), have been used to segment natural or medical objects, showing promising results. However, analyzing medical objects of small areas in images remains a challenge due to information losses and compression defects caused by convolution and pooling operations in CNNs. These losses and defects become increasingly significant as the network deepens, particularly for small medical objects. To address these challenges, we propose a novel scale-variant attention-based network (SvANet) for accurate small-scale object segmentation in medical images. The SvANet consists of Monte Carlo attention, scale-variant attention, and vision transformer, which incorporates cross-scale features and alleviates compression artifacts for enhancing the discrimination of small medical objects. Quantitative experimental results demonstrate the superior performance of SvANet, achieving 96.12%, 96.11%, 89.79%, 84.15%, 80.25%, 73.05%, and 72.58% in mean Dice coefficient for segmenting kidney tumors, skin lesions, hepatic tumors, polyps, surgical excision cells, retinal vasculatures, and sperms, which occupy less than 1% of the image areas in KiTS23, ISIC 2018, ATLAS, PolypGen, TissueNet, FIVES, and SpermHealth datasets, respectively.