This is known as a vexatious complaint.
If there is evidence to suggest the grievance was made with vexatious intent, then you may be able to follow your disciplinary procedures to deal with the matter as potential gross misconduct, however you do need to be careful.
If the employee made the complaint in good faith, then you may find yourself dealing with a tribunal claim later down the line.
Employers are expected to investigate any grievance with an open mind, before reaching a decision.
If you require further guidance on dealing with a possible malicious grievance, take professional advice.