documentclass[11.5pt]{report}
usepackage[usenames,dvipsnames] {xcolor}
usepackage[framemethod=TikZ]{mdframed}
usetikzlibrary{shadows}
usepackage{environ}
usepackage{varwidth}

newlength{MyMdframedWidthTweak}%
NewEnviron{MyMdframed}[1][]{%
    setlength{MyMdframedWidthTweak}{dimexpr%
        +mdflength{innerleftmargin}
        +mdflength{innerrightmargin}
        +mdflength{leftmargin}
        +mdflength{rightmargin}
        }%
    savebox0{%
        begin{varwidth}{dimexprlinewidth-MyMdframedWidthTweakrelax}%
            BODY
        end{varwidth}%
    }%
    begin{mdframed}[
        backgroundcolor=lightgray,
        shadow=true,
        shadowsize=4pt,
        roundcorner=5pt,
        userdefinedwidth=dimexprwd0+MyMdframedWidthTweakrelax,
        #1]
        usebox0
    end{mdframed}
}

begin{document}

begingroup
centering
begin{minipage}[c]{5in}
begin{MyMdframed}[backgroundcolor=blue!10]
    blah blah blah
end{MyMdframed}
end{minipage}
endgroup

end{document}