You need to "sneak" a \newpage into the ToC using \addtocontents{toc}{\protect\newpage}. Here is a minimal example showing the difference - bottom 2-page layout shows the addition of the \newpage:

\documentclass{memoir}% http://ctan.org/pkg/memoir
\begin{document}
\tableofcontents
\chapter{First chapter}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
%\addtocontents{toc}{\protect\newpage} % Adds \newpage in "\tableofcontents"
\chapter{Another chapter}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\section{A section}\section{A section}\section{A section}\section{A section}\section{A section}
\end{document}
It is usually required to \protect entries going into the ToC (or any external file, in general). For more on this, you should read What is the difference between Fragile and Robust commands?