We consider the Casimir effect for quantized massive scalar field with non-conformal coupling $\xi$ in a spacetime of wormhole whose throat is rounded by a spherical shell. In the framework of zetaregularization approach we calculate a zero point energy of scalar field. We found that depending on values of coupling $\xi$, a mass of field $m$, and/or the throat’s radius $a$ the Casimir force may be both attractive and repulsive, and even equals to zero.