My son is 7 months old and got a scratch that wouldn't stop bleeding and didn't know if i should use a band-aid since he is so small. I'm sure it's ok but thought i would get some in put.
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A Band-aid like any adhesive bandage has small risk of adhesive allergy. The adhesive used to hold a band-aid on can leave a mark if the child is allergic to it. It is a rare problem, but possible.

If you want to try a band-aid, use it for a short period of time and carefully take it off. Then watch the site for a day or two to see if anything happens there (like a rash or skin irritation.) If the skin looks unaffected, then the use of bandaids in the future will be less risky.

Source(s):
I am a Plastic Surgeon.