  The Palatini $f(|\hat{\Omega}|)$ gravity is a generalized theory of the
Eddington-inspired Born-Infeld gravity, where
$\Omega_{~N}^{K}\equiv\delta_{~N}^{K}+bg^{KL}R_{LN}(\Gamma)$ is an auxiliary
tensor constructed with the spacetime metric $g$ and independent connection
$\Gamma$. In this paper, we study $f(|\hat{\Omega}|)$ theory with
$f(|\hat{\Omega}|)=|\hat{\Omega}|^{\frac{1}{2}+n}$ in the thick brane scenario
and give some constraints on the brane model. We finally found an analytic
solution of the thick brane generated by a single scalar field. The behavior of
the negative energy density denotes the localization of the thick brane at the
origin of the extra dimension. In our braneworld, the warp factor is divergent
at the boundary of the extra dimension while the brane system is asymptotically
anti$-$de Sitter. It is shown that the tensor perturbation of the brane is
stable and the massless graviton is localized on the thick brane. Therefore,
the effective Einstein-Hilbert action on the brane can be rebuilt in the
low-energy approximation. According to the recent test of the gravitational
inverse-square law, we give some constraints on the $f(|\hat{\Omega}|)$ brane.
