We have investigated the noncentrosymmetric tetragonal heavy fermion compound $\mathrm{CeAuA}{\mathrm{l}}_{3}$ using muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$, neutron diffraction (ND), and inelastic neutron scattering (INS) measurements. We have also revisited the magnetic, transport, and thermal properties. The magnetic susceptibility reveals an antiferromagnetic transition at 1.1 K with, possibly, another magnetic transition near 0.18 K. The heat capacity shows a sharp $\ensuremath{\lambda}$-type anomaly at 1.1 K in zero field, which broadens and moves to a higher temperature in an applied magnetic field. Our zero-field $\ensuremath{\mu}\mathrm{SR}$ and ND measurements confirm the existence of a long-range magnetic ground state below 1.2 K. Further, the ND study reveals an incommensurate magnetic order with a magnetic propagation vector $\mathbf{k}=(0,0,0.52(1))$ and a spiral structure of Ce moments coupled ferromagnetically within the $ab$ plane. Our INS study reveals the presence of two well-defined crystal electric field (CEF) excitations at 5.1 and 24.6 meV in the paramagnetic phase of $\mathrm{CeAuA}{\mathrm{l}}_{3}$ that can be explained on the basis of the CEF theory and the Kramer's theorem for a Ce ion having a $4{f}^{1}$ electronic state. Furthermore, low energy quasielastic excitations show a Gaussian line shape below 30 K compared to a Lorentzian line shape above 30 K, indicating a slowdown of spin fluctuations below 30 K. We have estimated a Kondo temperature of ${T}_{\mathrm{K}}=3.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ from the quasielastic linewidth, which is in good agreement with that estimated from the heat capacity. This study also indicates the absence of any CEF-phonon coupling unlike that observed in isostructural $\mathrm{CeCuA}{\mathrm{l}}_{3}$ The CEF parameters, energy level scheme, and their wave functions obtained from the analysis of INS data explain satisfactorily the single crystal susceptibility in the presence of two-ion anisotropic exchange interaction in $\mathrm{CeAuA}{\mathrm{l}}_{3}$.