  We study the Casimir effect in the framework of Standard Model Extension
(SME). Employing the weak field approximation, the vacuum energy density
{\epsilon} and the pressure for a massless scalar field confined between two
nearby parallel plates in a static spacetime background are calculated. In
particular, through the analysis of {\epsilon}, we speculate a constraint on
the Lorentz-violating term s00 which is lower than the bounds currently
available for this quantity. After that, the correction to the pressure given
by the gravitational sector of SME is presented. Finally, we remark that our
outcome has an intrinsic validity that goes beyond the treated case of a
point-like source of gravity.
