Delving into pruning techniques is essential to boost the efficiency of Large Language Models (LLMs) by reducing their size and computational demands, resulting in faster and more cost-effective inference. In this work, our key contribution lies in recognizing that LLMs trained on diverse languages manifest distinct language-specific weight distributions. Exploiting this insight, we illustrate that pruning LLMs using language-specific data results in a more potent model compression. Empirical evidence underscores the critical nature of pruning on language-specific data, highlighting a noteworthy impact on the perplexity of Ukrainian texts compared to pruning on English data. The proposed methodology significantly reduces the size of LLaMA, LLaMA 2 and Mistral models while preserving competitive performance. This research underscores the significance of linguistic considerations in LLM pruning and advocates for language-specific optimization, establishing a framework for more efficient and tailored language models across diverse linguistic contexts. Additionally, all experiments were conducted using a single consumer-grade NVIDIA RTX 3090 GPU, and the code is available at https://github.com/mshamrai/language-specific-pruning.