  We observe an unconventional superconducting minigap induced into a
ferromagnet SrRuO$_3$ from a spin-triplet superconductor Sr$_2$RuO$_4$ using a
Au/SrTiO$_3$/SrRuO$_3$/Sr$_2$RuO$_4$ tunnel junction. Voltage bias differential
conductance of the tunnel junctions exhibits V-shaped gap features around zero
bias, corresponding to a decrease in the density-of-states with an opening of a
superconducting minigap in SrRuO$_3$. Observation of a minigap at a surface of
a 15~nm thick SrRuO$_3$ layers confirms the spin-triplet nature of induced
superconductivity. The shape and temperature dependence of the gap features in
the differential conductance indicate that the even-frequency $p$-wave
correlations dominate, over odd-frequency $s$-wave correlations. Theoretical
calculations support this $p$-wave scenario. Our work provides the
density-of-states proof for $p$-wave Cooper pair penetration in a ferromagnet
and significantly put forward our understanding of the $p$-wave spin-triplet
proximity effect between spin-triplet superconductors and ferromagnets.
