Infrared Small Target Detection (IRSTD) refers to detecting faint targets in infrared images, which has achieved notable progress with the advent of deep learning. However, the drive for improved detection accuracy has led to larger, intricate models with redundant parameters, causing storage and computation inefficiencies. In this pioneering study, we introduce the concept of utilizing network pruning to enhance the efficiency of IRSTD. Due to the challenge posed by low signal-to-noise ratios and the absence of detailed semantic information in infrared images, directly applying existing pruning techniques yields suboptimal performance. To address this, we propose a novel wavelet structure-regularized soft channel pruning method, giving rise to the efficient IRPruneDet model. Our approach involves representing the weight matrix in the wavelet domain and formulating a wavelet channel pruning strategy. We incorporate wavelet regularization to induce structural sparsity without incurring extra memory usage. Moreover, we design a soft channel reconstruction method that preserves important target information against premature pruning, thereby ensuring an optimal sparse structure while maintaining overall sparsity. Through extensive experiments on two widely-used benchmarks, our IRPruneDet method surpasses established techniques in both model complexity and accuracy. Specifically, when employing U-net as the baseline network, IRPruneDet achieves a 64.13% reduction in parameters and a 51.19% decrease in FLOPS, while improving IoU from 73.31% to 75.12% and nIoU from 70.92% to 74.30%. The code is available at https://github.com/hd0013/IRPruneDet.