As mentioned by Torbjørn T. minted has some options to add a frame. However minted doesn't do the frame. This is done by the package fancyvrb. The possibilities of frames with fancyvrb are limited. If you want e.g. round corners you can use another package like tcolorbox or mdframed.
The example below shows you the usage of tcolorbox. I am using the advantages of etoolbox to add a frame around every minted environment.
\documentclass[a5paper]{article}
\usepackage[]{minted}
\usepackage{tcolorbox}
\usepackage{etoolbox}
\BeforeBeginEnvironment{minted}{\begin{tcolorbox}}%
\AfterEndEnvironment{minted}{\end{tcolorbox}}%
\begin{document}
\begin{minted}{latex}
%Preamble
\usepackage[]{minted}
\usepackage{tcolorbox}
\usepackage{etoolbox}
\BeforeBeginEnvironment{minted}%
{\begin{tcolorbox}}%
\AfterEndEnvironment{minted}
{\end{tcolorbox}}%
\end{minted}
\end{document}

EDIT: If you want to have automatic line breaks with fancyvrb you can use the following. Please note line breaks only occur at spaces. A line break has pre hook in form of $\rightarrow$. You can change it, of course. To get the symbol in front of a line I used lineno.
\documentclass[a5paper]{article}
%\pagestyle{empty}
\usepackage[T1]{fontenc}
\usepackage[]{minted}
\usepackage{tcolorbox}
\usepackage{lineno}
\def\gobble#1{}
\renewcommand\DeleteFile[1]{}
\usepackage{xparse}
\ExplSyntaxOn
\box_new:N \l_fvrb_box
\tl_new:N \l_fvrb_tl
\RenewDocumentCommand \FancyVerbFormatLine { m }
{
\hbox_set:Nn \l_fvrb_box { #1 }
\dim_compare:nNnTF { \box_wd:N \l_fvrb_box }>{ \linewidth }
{%box to big
\tl_set:Nn \l_fvrb_tl { #1 }
\fvrb_use_tl:N \l_fvrb_tl
}
{%box fits
\box_use:N \l_fvrb_box
}
}
\cs_new:Npn \fvrb_use_tl:N #1
{
\group_begin:
\null\hfill\vbox_set:Nn \l_fvrb_box
{\hsize=\linewidth
\renewcommand\thelinenumber
{
\ifnum\value{linenumber}=1\relax\else
$\rightarrow$
\fi
}
\begin{internallinenumbers}
\advance\hsize by -2em
\hspace*{-2em}\tl_use:N #1
\end{internallinenumbers}
}
\box_use:N \l_fvrb_box
\group_end:
}
\ExplSyntaxOff
\usepackage{etoolbox}
\BeforeBeginEnvironment{minted}{\begin{tcolorbox}}%
\AfterEndEnvironment{minted}{\end{tcolorbox}}%
\begin{document}
\begin{minted}{latex}
%Preamble
\usepackage[]{minted}
\usepackage[fancyvrb=true]{listings}
\usepackage{tcolorbox}
\usepackage{etoolbox}
\BeforeBeginEnvironment {minted} { \begin{tcolorbox} } \AfterEndEnvironment {minted} { \end{tcolorbox} }%
\usepackage{lipsum}
\end{minted}
\end{document}

\documentclass{...}and ending with\end{document}. – Marco Daniel May 05 '13 at 11:05