  The recently discovered (Ba,Sr)Ni$_2$As$_2$ family provides an ideal platform
for investigating the interaction between electronic nematicity and
superconductivity. Here we report the muon spin relaxation ($\mu$SR)
measurements on BaNi$_2$As$_2$. Transverse-field $\mu$SR experiments indicate
that the temperature dependence of superfluid density is best fitted with a
single-band $s$-wave model. On the other hand, the magnetic penetration depth
$\lambda$ shows magnetic field dependence, which contradicts with the
single-band fully-gapped scenario. Zero-field $\mu$SR experiments indicate the
absence of spontaneous magnetic field in the superconducting state, showing the
preservation of time-reversal symmetry in the superconducting state. Our
$\mu$SR experiments suggest that BaNi$_2$As$_2$ is a fully-gapped multiband
superconductor. The superconducting gap amplitudes of each band are nearly the
same while different bands exhibit different coherence lengths. The present
work helps to elucidate the controversial superconducting property of this
parent compound, paving the way for further research on doping the system with
Sr to enhance superconductivity.
