The low-lying level structure of $^{41}\mathrm{K}$ has been studied using the thermal-neutron capture reaction $^{40}\mathrm{K}(n,\ensuremath{\gamma})^{41}\mathrm{K}$ on an isotopically separated target of $^{40}\mathrm{K}$. The $\ensuremath{\gamma}$-ray spectrum from this reaction has been studied in the energy range from 0.1 to 10.1 MeV using a Li-drifted Ge spectrometer system. $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidence measurements using Ge(Li) detectors have also been made. Spin and parity assignments for the excited states below 2450 keV are proposed, primarily on the basis of $\ensuremath{\gamma}$-ray branching to levels with established spin and parity values. The proposed level energy [keV (${I}^{\ensuremath{\pi}}$)] values are $0({\frac{3}{2}}^{+})$, $980.4({\frac{1}{2}}^{+})$, $1293.4({\frac{7}{2}}^{\ensuremath{-}})$, $1559.9({\frac{1}{2}}^{+})$, $1582.0({\frac{5}{2}}^{+})$, $1677.5({\frac{5}{2}}^{+},{\frac{7}{2}}^{+})$, $1698.1({\frac{5}{2}}^{\ifmmode\pm\else\textpm\fi{}},{\frac{7}{2}}^{+})$, $2144.1({\frac{5}{2}}^{+})$, $2166.0({\frac{1}{2}}^{+},{\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}})$, $2316.5({\frac{5}{2}}^{+},{\frac{7}{2}}^{+})$, $2447.9({\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}},{\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}})$. Additional levels have been observed at 2494.7, 2507.9, 2527.9, 2599.8, 2681.5, 2712.2, 2756.5, 2760.7, 3042.1, 3142.1, 3164.5, 3213.4, 3235.6, and 3281.1 keV. These low-lying excited states of $^{41}\mathrm{K}$ are discussed in terms of two-particle, one-hole configurations of the form $p{({d}_{\frac{3}{2}})}^{\ensuremath{-}1}n{({f}_{\frac{7}{2}})}^{2}$.