It looks like Instagram followed in its parent company Facebook’s footsteps and added a secret inbox.
Much like Facebook’s “Filtered” and “Message Requests” folders, Instagram has a separate inbox in its Direct Messages feature for posts from strangers (i.e. people you don’t follow) so that you’re not waking up to unsolicited comments or online harassment. Instagram doesn’t send you a notification when you get these messages, and you need to officially accept a message request from a stranger to be able to open and read it.
Finding this hidden inbox is easy. Once you’re logged into Instagram, click the box icon in the upper right-hand corner, which opens up your Direct Messages. If someone you don’t follow has messaged you, a blue banner will appear showing you a message request. From there, click “Allow” to accept the request and see the message and “Decline” to reject it.
And if someone keeps bothering you, keep in mind that Instagram makes it easy for you to go to any user’s profile and block that person, so you’ll never receive those unwanted messages again.
Related: Instagram Just Got a Major Makeover