Yes, MIA offers a 24-hour Left Item Service. This is another service for added convenience. Offered at a flat rate of €5, the Left Item Service can be availed of to deposit an item that fits in an A4 envelope, which may be picked up later by the person depositing the item or by someone on their behalf within 30 days of their deposit.
Further information may be found here:
https://www.maltairport.com/passenger/services/luggage-deposit-and-left-item-services/