Yes you can. You can set a PIN on your whole My Health Record so that your health provider has to have you in the room before they can access it. You can also lock down individual documents.
My Health Record's security settings allow restrictions on which individuals (such as family members) can see your information, and what information your healthcare providers can access, and more. For example, you may not want your pharmacist to view information about a mental health condition. You also have the option to lock individual documents held on the system, so information you feel is sensitive can be restricted. Setting a passcode on these documents means you can control who sees them, and when.
See here for more information or check this Privacy Fact Sheet from the Office of the Australian Information Commissioner.