  We calculate the full set of next-to-leading order (NLO) corrections to $h\to
b\bar{b}$ decay in the dimension-6 Standard Model Effective Field Theory
(SMEFT). Our calculation forms the basis for precision studies of this decay
mode in effective field theory, providing analytic and numerical results for
contributions of the 45 dimension-6 operators appearing at NLO. On the
technical side, we discuss several complications in NLO SMEFT computations
which have not yet been addressed in the literature. These include subtleties
in Higgs-$Z$ mixing, electric charge renormalization, and especially the
treatment of tadpoles in SMEFT. In particular, we highlight the role of
decoupling relations in eliminating potentially large tadpole corrections to
the decay rate in hybrid renormalization schemes which employ the
$\overline{\hbox{MS}}$~scheme for some Standard Model parameters (such as the
$b$-quark mass and electric charge) and the on-shell scheme for others.
