  New physics can emerge at low energy scales, involving very light and very
weakly interacting new particles. These particles can mediate interactions
between neutrinos and usual matter and contribute to the Wolfenstein potential
relevant for neutrino oscillations. We compute the Wolfenstein potential in the
presence of ultra-light scalar and vector mediators and study the dependence of
the potential on the mediator mass $m_A$, taking the finite size of matter
distribution (Earth, Sun, supernovae) into consideration. For ultra-light
mediators with $m_{A}^{-1}$ comparable to the size of the medium ($R$), the
usual $m_{A}^{-2}$ dependence of the potential is modified. In particular, when
$m_{A}^{-1}\gg R$, the potential does not depend on $m_{A}$. Taking into
account existing bounds on light mediators, we find that for the scalar case
significant effects on neutrino propagation are not possible, while for the
vector case large matter effects are allowed for $m_{A} \in [2\times10^{-17}$,
$4\times10^{-14}]$ eV and the gauge coupling $g\sim 10^{-25}$.
