In this paper we study the direct $CP$ asymmetry of the doubly Cabibbo-suppressed decay mode ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ within standard model and two Higgs doublet model with generic Yukawa structure. In the standard model we derive the corrections to the tree level amplitude, generated from the box and dipenguin diagrams, required for generating the weak $CP$ violating phases. We show that these phases are so tiny leading to a direct $CP$ asymmetry of order ${10}^{\ensuremath{-}9}$. Regarding the two Higgs doublet model with generic Yukawa structure we derive the Wilson coefficients relevant to ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. After taking into account all constraints on the parameter space of the model we show that charged Higgs couplings to quarks can lead to a direct $CP$ asymmetry of order ${10}^{\ensuremath{-}3}$ which is 6 orders of magnitude larger than the standard model prediction.