Glossaries conflict with memoir

Update to glossaries version 4.04 and use the noredefwarn package option:

\documentclass{memoir}

\usepackage[noredefwarn]{glossaries}

\makeglossaries

\begin{document}

Hello World

\printglossary

\end{document}

glossaries also has a nowarn option that suppresses warnings, but if something unexpected happens it's best to switch the warnings back on.

Edit: glossaries-extra enables this option by default:

\documentclass{memoir}

\usepackage{glossaries-extra}

\makeglossaries

\begin{document}

Hello World

\printglossary

\end{document}

With the same style as for \printglossary, you can use

\documentclass{memoir}

\let\printglossary\relax
\let\theglossary\relax
\let\endtheglossary\relax

\usepackage{glossaries}
\makeglossaries
\begin{document}
Hello World
\printglossary
\end{document}

I wouldn't silence off all warnings by glossaries. With silence you can override the relevant messages by

\documentclass{memoir}

\usepackage{silence}
\WarningFilter{glossaries}{Overriding \printglossary}
\WarningFilter{glossaries}{overriding `theglossary'}

\usepackage{glossaries}
\makeglossaries
\begin{document}
Hello World
\printglossary
\end{document}

You can use the package silence.

Issue \WarningsOff* before loading glossaries and \WarningsOn after it.

MWE:

\documentclass{memoir}
\usepackage{silence}
\WarningsOff*
\usepackage{glossaries}
\WarningsOn
\makeglossaries
\begin{document}
Hello World
\printglossary
\end{document} 

In this way those warnings are gone and all the rest of them in the document are still there.