We establish the functional convex order results for two scaled McKean–Vlasov processes $\mathit{X}={({\mathit{X}}_{\mathit{t}})}_{\mathit{t}\in [0,\mathit{T}]}$ and $\mathit{Y}={({\mathit{Y}}_{\mathit{t}})}_{\mathit{t}\in [0,\mathit{T}]}$ defined on a filtered probability space $(\mathrm{\Omega },\mathcal{F},{({\mathcal{F}}_{\mathit{t}})}_{\mathit{t}\ge 0},\mathbb{P})$ by

$$\left\{\begin{array}{ll}\mathit{d}{\mathit{X}}_{\mathit{t}}=\mathit{b}(\mathit{t},{\mathit{X}}_{\mathit{t}},{\mathit{\mu }}_{\mathit{t}})\mathit{d}\mathit{t}\mathbf{+}\mathit{\sigma }(\mathit{t},{\mathit{X}}_{\mathit{t}},{\mathit{\mu }}_{\mathit{t}})\mathit{d}{\mathit{B}}_{\mathit{t}},& {\mathit{X}}_0\in {\mathit{L}}^{\mathit{p}}(\mathbb{P}),\\ \mathit{d}{\mathit{Y}}_{\mathit{t}}=\mathit{b}(\mathit{t},{\mathit{Y}}_{\mathit{t}},{\mathit{\nu }}_{\mathit{t}})\mathit{d}\mathit{t}\mathbf{+}\mathit{\theta }(\mathit{t},{\mathit{Y}}_{\mathit{t}},{\mathit{\nu }}_{\mathit{t}})\mathit{d}{\mathit{B}}_{\mathit{t}},& {\mathit{Y}}_0\in {\mathit{L}}^{\mathit{p}}(\mathbb{P}),\end{array}\right.$$

where $\mathit{p}\ge 2$, for every $\mathit{t}\in [0,\mathit{T}]$, ${\mathit{\mu }}_{\mathit{t}}$, ${\mathit{\nu }}_{\mathit{t}}$ denote the probability distribution of ${\mathit{X}}_{\mathit{t}}$, ${\mathit{Y}}_{\mathit{t}}$ respectively and the drift coefficient $\mathit{b}(\mathit{t},\mathit{x},\mathit{\mu })$ is affine in x (scaled). If we make the convexity and monotony assumption (only) on σ and if $\mathit{\sigma }⪯\mathit{\theta }$ with respect to the partial matrix order, the convex order for the initial random variable ${\mathit{X}}_0{⪯}_{\mathit{c}\mathit{v}}{\mathit{Y}}_0$ can be propagated to the whole path of process X and Y. That is, if we consider a convex functional F defined on the path space with polynomial growth, we have $\mathbb{E}\mathit{F}(\mathit{X})\le \mathbb{E}\mathit{F}(\mathit{Y})$; for a convex functional G defined on the product space involving the path space and its marginal distribution space, we have $\mathbb{E}\mathit{G}(\mathit{X},{({\mathit{\mu }}_{\mathit{t}})}_{\mathit{t}\in [0,\mathit{T}]})\le \mathbb{E}\mathit{G}(\mathit{Y},{({\mathit{\nu }}_{\mathit{t}})}_{\mathit{t}\in [0,\mathit{T}]})$ under appropriate conditions. The symmetric setting is also valid, that is, if $\mathit{\theta }⪯\mathit{\sigma }$ and ${\mathit{Y}}_0\le {\mathit{X}}_0$ with respect to the convex order, then $\mathbb{E}\mathit{F}(\mathit{Y})\le \mathbb{E}\mathit{F}(\mathit{X})$ and $\mathbb{E}\mathit{G}(\mathit{Y},{({\mathit{\nu }}_{\mathit{t}})}_{\mathit{t}\in [0,\mathit{T}]})\le \mathbb{E}\mathit{G}(\mathit{X},{({\mathit{\mu }}_{\mathit{t}})}_{\mathit{t}\in [0,\mathit{T}]})$. The proof is based on several forward and backward dynamic programming principles and the convergence of the Euler scheme of the McKean–Vlasov equation. Two applications of these results, to mean field control and mean field games, are proposed.