A memristor is, by definition, an element whose constitutive relation is of the type [1]
$$g(\varphi,q)=0,$$
where $\varphi = \int_{-\infty}^t v(s)\,\mathrm{d}s$ is the flux linkage and $q= \int_{-\infty}^t i(s)\,\mathrm{d}s$ is the charge.
If the relationship $g(\varphi,q)=0$ is linear, the memristor degenerates into a linear resistor and, thus, its impedance coincides with the resistance.
When the relationship $g(\varphi,q)=0$ is nonlinear, the memristor becomes a nonlinear element for which the concept of impedance is valid only in the so-called small signal approximation, that is, when the applied signal around a certain operating point is sufficiently small that the nonlinearity can be neglected. This kind of linearization is well known in circuit theory, and, for instance, it is commonly applied when analyzing transistor amplifiers. Let's see how this can be done in the case of the memristor.
If the relationship $g(\varphi,q)=0$ can be solved for $\varphi$, that is, we can write $\varphi = f_\mathrm{M}(q)$ (at least in a certain interval) the memristor is called charge-controlled and its $iv$ characteristic is given by [1]
$$v = R(q)i,\qquad\qquad(1)$$
where
$$R(q) = \frac{\mathrm{d}f_\mathrm{M}(q)}{\mathrm{d} q}$$
is a charge-dependent resistance. Since $q= \int_{-\infty}^t i(s)\,\mathrm{d}s$, the charge $q$ at any given instant depends on the past history of the current. But once you have reached a certain operating point $q$, the one of interest, you can think of applying a sine wave with infinitely small amplitude, so that the charge remains virtually constant. Around this operating point, you can see from (1) that the voltage across the memristor is proportional to the current, that is, for small signals the memristor behaves like a resistor with differential resistance $R(q)$. Hence, the small signal impedance will be $R(q)$.
A more detailed analysis of the circuit behaviour of the memristor can be found in Chua's papers [1-3]. In [3], in particular, it is discussed the impedance.
[1] L. O. Chua, "Memristor - The missing circuit element," IEEE Trans. Circuit Theory, CT-18, 507–519, 1971.
[2] L. O. Chua, "The fourth element", Proc. IEEE, 100, 1920-1927, 2012.
[3] L. O. Chua, "Nonlinear circuit foundations for nano devices, Part I: The Four-Element torus," Proc. IEEE, 91, 1830–1859, 2003.