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Correlation networks derived from multivariate data appear in many applications across the sciences. These networks are usually dense and require sparsification to detect meaningful structure. However, current methods for sparsifying correlation networks struggle with balancing overfitting and underfitting. We propose a module-based cross-validation procedure to threshold these networks, making modular structure an integral part of the thresholding. We illustrate our approach using synthetic and real data and find that its ability to recover a planted partition has a step-like dependence on the number of data samples. The reward for sampling more varies non-linearly with the number of samples, with minimal gains after a critical point. A comparison with the well-established WGCNA method shows that our approach allows for revealing more modular structure in the data used here.