My employment contract with my employee states that I can provide 1 month notice to terminate employment at any time. Would I still need to notify MOM in this case?

Yes, if the worker is terminated (which means that the worker is dismissed on the ground of redundancy or by reason of any reorganisation of the employer’s profession, business, trade or work), the employer would still need to notify MOM within 5 working days after the employee has been notified of his or her retrenchment.