Go to Profile → Settings → Privacy to control who can interact with your content.
Private Account
When enabled, only approved followers can see your posts. New follow requests must be manually approved by you. Your profile will show a lock icon to indicate it's private.
Who Can Comment
Choose from: Everyone / Followers only / No one Controls who is allowed to leave comments on your posts.
Who Can Message You
Choose from: Everyone / Followers only / No one Controls who can send you direct messages. (Messaging coming soon.)