Children often use security items to help them cope with stress. Times of major change such as moving, starting a new school, or becoming a big sibling, can cause stress in young children. Some kids deal with stress by latching on to an item that brings them comfort.
I see no harm in allowing him to wear his beloved shirt until the phase passes. Soon, he'll tire of the shirt and develop the skills he needs to comfort himself without it. In the meantime, you'll have to ensure that the shirt is clean everyday. Wash it often and buy an extra, identical shirt. More importantly, find out why he feels the need for this comfort item, and see if you can help him deal with stress in a different way.