Is it permissible for the muezzin to interrupt the call to prayer (adhan) to say "Yarhamukallah" (may Allah have mercy on you) to someone who sneezes?

Brief speech that is not religiously required is disliked during the Adhan. As for speech that is religiously required, such as returning a greeting (salaam) or saying "Yarhamukallah" to someone who sneezes, there is a difference of opinion among the madhhabs (schools of thought).

Hanafis: Brief speech is disliked absolutely. Shafi'is: It is contrary to what is superior (khilaf al-awla). Hanbalis: It is permissible. Malikis: It is disliked, and one should not interrupt the words of the Adhan with speech or returning a greeting, even by gesture.