Muslim scholars state that there is nothing wrong with wearing a sling to carry a baby during ihram, as such an act resembles carrying a waterskin or a purse, which is not forbidden. The prominent Saudi Islamic lecturer and author Sheikh Muhammad Saleh Al-Munajjid states the following:
There is nothing wrong with wearing a sling to carry a baby while in ihram, because that is not the kind of clothing that is described in the texts as being forbidden when in ihram, nor is it like such clothing. It is more like carrying a waterskin or a purse, or carrying one’s luggage on one’s back tied with a rope around the chest. These things are not forbidden.
The clothes that are forbidden [for men] during ihram are shirts, pants, burnous (a wide garment with an attached hood to cover the head), turbans, and khufuf (leather slippers). The evidence for that is the hadith reported by `Abdullah ibn `Umar (may Allah be pleased with him): A man stood up and said, “O Messenger of Allah, what do you command us to wear when we enter ihram?” He said, “Do not wear a shirt, pants, a turban, a burnous or khufuf, unless a man does not have any sandals, in which case he may wear khufuf that come below the ankle. And do not wear any garment that has been dyed with saffron or wars (safflower).”
With the above in mind, it can be said that carrying a baby with a sling is like carrying a waterskin or carrying one’s luggage on the back tied with a rope around the chest if necessary. Moreover, some scholars stated that it is permissible for a person in ihram to carry his luggage on his back and to tie it with a rope around the chest if necessary. This is very much like a sling for carrying a child.