Treatment for mosquito bite on infant

Nothing specific. If the infant is not uncomfortable no specific treatment is indicated. If the baby tends to get large local reactions to insect bites ice should be put on the bite asap. Benadryl (diphenhydramine) by mouth can also be given for extreme swelling or itchiness as well as a low dose cortisone cream.
Watch for infection. Nothing specific needs to be done, but you want to be sure to watch carefully for any signs of infection. Infants' nerve endings are not as sensitive as older children and adults, so the itching sensation will not bother them. However, if they seem uncomfortable a cold compress on the area will help. Signs of infection include increasing redness, swelling, warmth and any pus by the bite.
Some lotions help. I'm partial to gold bond medicated lotion myself (in the green bottle). It contains menthol, which is a mild local anaesthetic, and thus decreases itching. It was very helpful to me personally after i was stung by wasps over 60 times, and i've recommended it since. You can't overdose the stuff, and the worst that happens if you use too much is your baby feels greasy.