  Temperature dependent $^{57}$Fe M\"ossbauer spectroscopy and specific heat
measurements for CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ with $x$ = 0, 0.017, 0.033,
and 0.049 are presented. No magnetic hyperfine field (e.g. no static magnetic
order) down to 5.5 K was detected for $x$ = 0 and 0.017 in agreement with the
absence of any additional feature below superconducting transition temperature,
$T_c$, in the specific heat data. The evolution of magnetic hyperfine field
with temperature was studied for $x$ = 0.033 and 0.049. The long-range magnetic
order in these two compounds coexists with superconductivity. The magnetic
hyperfine field, $B_{hf}$, (ordered magnetic moment) below $T_c$ in
CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$ is continuously suppressed with the
developing superconducting order parameter. The $B_{hf}(T)$ data for
CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$, and
CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$ can be described reasonably well by
Machida's model for coexistence of itinerant spin density wave magnetism and
superconductivity [K. Machida, J. Phys. Soc. Jpn. {\bf 50}, 2195 (1981)]. We
demonstrate directly that superconductivity suppresses the spin density wave
order parameter if the conditions are right, in agreement with the theoretical
analysis.
