  We introduce codimension three magnetically charged surface operators in
five-dimensional (5d) $\mathcal{N}=1$ supersymmetric gauge on $T^2 \times
\mathbb{R}^3$. We evaluate the vacuum expectation values (vevs) of surface
operators by supersymmetric localization techniques. Contributions of Monopole
bubbling effects to the path integral are given by elliptic genera of world
volume theories on D-branes. Our result gives an elliptic deformation of the
SUSY localization formula \cite{Ito:2011ea} (resp. \cite{Okuda:2019emk,
Assel:2019yzd}) of BPS 't Hooft loops (resp. bare monopole operators) in 4d
$\mathcal{N}=2$ (resp. 3d $\mathcal{N}=4$) gauge theories. We define
deformation quantizations of vevs of surface operators in terms of the
Weyl-Wigner transform, where the $\Omega$-background parameter plays the role
of the Planck constant. For 5d $\mathcal{N}=1^*$ gauge theory, we find that the
deformation quantization of the surface operators in the anti-symmetric
representations agrees with the type A elliptic Ruijsenaars operators. The
mutual commutativity of these difference operators is related to the
commutativity of products of 't Hooft surface operators.
