대략 다음과 같이 하면 어떨까요? 현재 컬럼이 두 개인데 이를 셋으로 쪼개는 겁니다. 

첫 번째 컬럼은 그림만 놓고, 두 번째/ 세 번째 컬럼은 p 정렬(이게 디폴트)로.

\documentclass{memoir}

\usepackage{fapapersize}

\usepackage{graphicx}

\usepackage{tabu}

\usefapapersize{210mm,297mm,20mm,20mm,20mm,30mm}

\graphicspath{{img/}{img/Layout/}{img/icon/}}

\begin{document}

\tabulinesep=3mm

\tabulinestyle{.3mm}

\begin{tabu}{|X[.3,r,m]X[.5,l,p]|[.2mm]X[4,l,p]|}

\tabucline[]{-}

\includegraphics[scale=1]{warning} &Warning & This package defines a single environment tabu to make all kinds of tabulars \\

\tabucline[]{-}

\includegraphics[scale=1]{caution}&Caution & This package defines a single environment tabu to make all kinds of tabulars in text or in math mode

provided that they do not split across pages.\\

\tabucline[]{-}

\includegraphics[scale=1]{prohibit}& & This package defines a single environment tabu to make all kinds of tabulars in text or in math mode

provided that they do not split across pages.\\

\tabucline[]{-}

\includegraphics[scale=1]{exclamation}& & This package defines a single environment tabu to make all kinds of tabulars.\\

\tabucline[]{-}

\end{tabu}

\end{document}