Use aws_ssm module for this purpose:
- name: example
  rabbitmq_user:
    user: "{{ lookup('aws_ssm', 'user', region='us-east-1') }}"
    password: "{{ lookup('aws_ssm', 'password', region='us-east-1') }}
    state: present
    force: yes
  become: yes
  become_method: sudo
  become_user: root
  register: example
  notify:
    - restart rabbitmq-server