Voice assistants have become ubiquitous in smart devices allowing users to instantly access information via voice questions. While extensive research has been conducted in question answering for voice search, little attention has been paid on how to enable proactive recommendations from a voice assistant to its users. This is a highly challenging problem that often leads to user friction, mainly due to recommendations provided to the users at the wrong time. We focus on the domain of e-commerce, namely in identifying Shopping Product Questions (SPQs), where the user asking a product-related question may have an underlying shopping need. Identifying a user's shopping need allows voice assistants to enhance shopping experience by determining when to provide recommendations, such as product or deal recommendations, or proactive shopping actions recommendation. Identifying SPQs is a challenging problem and cannot be done from question text alone, and thus requires to infer latent user behavior patterns inferred from user's past shopping history. We propose features that capture the user's latent shopping behavior from their purchase history, and combine them using a novel Mixture-of-Experts (MoE) model. Our evaluation shows that the proposed approach is able to identify SPQs with a high score of F1=0.91. Furthermore, based on an online evaluation with real voice assistant users, we identify SPQs in real-time and recommend shopping actions to users to add the queried product into their shopping list. We demonstrate that we are able to accurately identify SPQs, as indicated by the significantly higher rate of added products to users' shopping lists when being prompted after SPQs vs random PQs.