This paper aims to investigate the existence and properties of
anisotropic quark stars in the context of self-interacting
Brans-Dicke theory. In this theory, the gravitational constant in
general relativity is replaced by a dynamical massive scalar field
accompanied by a potential function. Researchers believe that
strange stars may evolve from neutron stars when neutrons fail to
endure the extreme temperature and pressure in the interior region.
As a consequence they breakdown into their constituent particles
known as quarks. In order to construct a well-behaved quark star
model under the influence of massive scalar field, we formulate the
field equations by employing the MIT bag model. The MIT bag model
(strange quark matter equation of state) is the most suitable choice
for quark stars as it has successfully described the compactness of
certain stellar bodies. Furthermore, the estimates of mass of quark
stars based on the data from the cosmic events GW170817 and GW190425
support the choice of MIT bag model. The model is developed by
considering three types of quark matter: strange, up and down. The
bag constant involved in the model differentiates between false and
true vacuum. We consider a static sphere with anisotropic fluid and
employ the observed masses and radii of the strange star candidates
(RXJ 1856-37 and PSR J1614-2230) in the matching conditions at the
boundary to evaluate the value of bag constant. Further, we evaluate
the impact of the massive scalar field on state parameters and
investigate the viability (via energy conditions) as well as
stability (through the speed of sound constraints) of the
self-gravitating objects. It is found that the obtained values of
the bag constant lie within the accepted range
($58.9MeV/fm^3\leq\mathcal{B}\leq91.5MeV/fm^3$). Moreover, the
anisotropic structure meets the necessary viability and stability
criteria.