We build an emulator based on the polynomial chaos expansion (PCE) technique to efficiently model the non-linear effects associated with the clustering of the k-essence dark energy in the effective field theory framework. These effects can be described through a modification of Poisson’s equation, denoted by the function $\mu (k,z)$, which in general depends on wavenumber k and redshift z. To emulate this function, we perform 200 high-resolution N-body simulations sampled from a seven-dimensional parameter space with the Latin hypercube method. These simulations are executed using the k-evolution code on a fixed mesh, containing $1200^3$ dark matter particles within a box size of $400~\text{Mpc}\, h^{-1}$. The emulation process has been carried out within uqlab, a matlab-based software specifically dedicated to emulation and uncertainty quantification tasks. Apart from its role in emulation, the PCE method also facilitates the measurement of Sobol indices, enabling us to assess the relative impact of each cosmological parameter on the $\mu$ function. Our results show that the PCE-based emulator efficiently and accurately reflects the behaviour of the k-essence dark energy for the cosmological parameter space defined by $w_0 c_\mathrm{ s}^2 \text{CDM} +\sum m_{\nu }$. Compared against actual simulations, the emulator achieves sub-per cent accuracy up to the wavenumber $k \approx 9.4 ~h\, \text{Mpc}^{-1}$ for redshifts $z \le 3$. Our emulator provides an efficient and reliable tool for Markov chain Monte Carlo analysis, and its capability to closely mimic the properties of the k-essence dark energy makes it a crucial component in Bayesian parameter estimations. The code is publicly available at https://github.com/anourizo/k-emulator.