  We develop some basic properties such as $p$-centers of affine vertex
algebras and free field vertex algebras in prime characteristic. We show that
the Wakimoto-Feigin-Frenkel homomorphism preserves the $p$-centers by providing
explicit formulas. This allows us to formulate the notion of baby Wakimoto
modules, which in particular provides an interpretation in the context of
modular vertex algebras for Mathieu's irreducible character formula of modular
affine Lie algebras at the critical level.
