  We investigate the effects of non-Newtonian gravity on the properties of
strange quark stars (QSs) and constrain the parameters of the standard MIT bag
model used to describe strange quark matter (SQM) by employing the mass of PSR
J0740+6620 and the tidal deformability of GW170817. We find that, for the
standard MIT bag model, these mass and tidal deformability observations would
rule out the existence of QSs if non-Newtonian gravity effects are ignored. For
a strange quark mass of $m_{s}=95$ MeV, we find that QSs can exist for values
of the non-Newtonian gravity parameter $g^{2}/\mu^{2}$ in the range of 1.37
GeV$^{-2}\leq g^{2}/\mu^{2}\leq$ 7.28 GeV$^{-2}$ and limits on the bag constant
and the strong interaction coupling constant of the SQM model given by 141.3
MeV$\leq B^{1/4}\leq$ 150.9 MeV and $\alpha_{S}\leq 0.56$. For a strange quark
mass of $m_{s}=150$ MeV, QSs can exist for 1.88 GeV$^{-2}\leq
g^{2}/\mu^{2}\leq$ 6.27 GeV$^{-2}$ and limits on the parameters of the SQM
model given by 139.7 MeV$\leq B^{1/4}\leq$ 147.3 MeV and $\alpha_{S}\leq 0.49$.
