The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono ([5, Problem 7.30]). As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strong...