Multimedia-based recommendation provides personalized item suggestions by learning the content preferences of users. With the proliferation of digital devices and APPs, a huge number of new items are created rapidly over time. How to quickly provide recommendations for new items at the inference time is challenging. What's worse, real-world items exhibit varying degrees of modality missing(e.g., many short videos are uploaded without text descriptions). Though many efforts have been devoted to multimedia-based recommendations, they either could not deal with new multimedia items or assumed the modality completeness in the modeling process. In this paper, we highlight the necessity of tackling the modality missing issue for new item recommendation. We argue that users' inherent content preference is stable and better kept invariant to arbitrary modality missing environments. Therefore, we approach this problem from a novel perspective of invariant learning. However, how to construct environments from finite user behavior training data to generalize any modality missing is challenging. To tackle this issue, we propose a novel Multimodality Invariant Learning reCommendation(a.k.a. MILK) framework. Specifically, MILK first designs a cross-modality alignment module to keep semantic consistency from pretrained multimedia item features. After that, MILK designs multi-modal heterogeneous environments with cyclic mixup to augment training data, in order to mimic any modality missing for invariant user preference learning. Extensive experiments on three real datasets verify the superiority of our proposed framework. The code is available at https://github.com/HaoyueBai98/MILK.