Multilingual speech data often suffer from long-tailed language distribution, resulting in performance degradation. However, multilingual text data is much easier to obtain, yielding a more useful general language model. Hence, we are motivated to distill the rich knowledge embedded inside a well-trained teacher text model to the student speech model. We propose a novel method called the Distilling a Language model to a Speech model (Distill-L2S), which aligns the latent representations of two different modalities. The subtle differences are handled by the shrinking mechanism, nearest-neighbor interpolation, and a learnable linear projection layer. We demonstrate the effectiveness of our distillation method by applying it to the multilingual automatic speech recognition (ASR) task. We distill the transformer-based cross-lingual language model (InfoXLM) while fine-tuning the large-scale multilingual ASR model (XLSR-wav2vec 2.0) for each language. We show the superiority of our method on 20 low-resource languages of the CommonVoice dataset with less than 100 hours of speech data.