Caption package not working with beamer

You don't need the caption package for this.

Simply issue the command

\setbeamerfont{caption}{size=\footnotesize}

MWE

\PassOptionsToPackage{demo}{graphicx} % remove in your document
\documentclass{beamer}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{lmodern}% http://ctan.org/pkg/lm
\graphicspath{{images/}}
\usetheme{default}

\setbeamerfont{caption}{size=\footnotesize}

\begin{document}
\begin{frame}
\begin{figure}[h]
  \centering
  \includegraphics[scale=0.8]{axb-grid}
  \caption{$A \times B$ grid}
  \label{fig:axbgrid}
\end{figure}
\end{frame}
\end{document} 

Output:

---

EDIT

While with old versions of beamer, caption commands used to work, it seems that now the caption package is not able to recognize beamer anymore.

In fact, loading caption with beamer you get the following warning:

Package caption Warning: \caption will not be redefined since it's already

(caption) redefined by a document class or package which is

(caption) unknown to the caption package.

See the caption package documentation for explanation.

If you want caption and its \captionsetup to work with beamer, you have to load caption with the option compatibility=false:

\usepackage[compatibility=false]{caption}

but, as the documentation warns:

But please note that using this option is neither recommended nor supported since unwanted side-effects or even errors could occur afterwards.

These Issues have been cleared and should be closed in 2019 versions of the packages

Please update to Tex Live 2019 (Note W32TeX / MiKTeX are generally already updated)