Amazon does a pretty good job following up with customers who buy products on their website. They ask them to take time and write a review. This doesn't always get seen by the customer since some of these follow-up emails go straight into a promotions folder for the email account.
However, you can take action and email your customers directly. Ask them how they like the product and if they are satisfied with their purchase. If they are, it never hurts to ask them to give an honest review of the product. This is also a good time to ask them to sign up for a product/brand newsletter or offer % discounts on their next purchase from your own eCommerce website (if you have one setup). You can setup an email autoresponder like Aweber or Mail Chimp to automate this process for you.