You can use
\let\oldsquare\square
before loading mathabx and then use \oldsquare in your definition:
\documentclass[11pt]{article}
\usepackage{amssymb}
\let\oldsquare\square
\usepackage{mathabx}
\newenvironment{prf}{\underline{\textbf{Proof:}}}{\hfill$\oldsquare$}
\begin{document}
\begin{prf}
This is my proof using mathabx.
\end{prf}
\end{document}

The proof environment from the amsthm package doesn't use \square, but \openbox as the end-mark, so you can define this command as amsthm.sty does and use it for your definition:
\documentclass[11pt]{article}
\usepackage{amssymb}
\usepackage{mathabx}
\newcommand{\openbox}{\leavevmode
\hbox to.77778em{%
\hfil\vrule
\vbox to.675em{\hrule width.6em\vfil\hrule}%
\vrule\hfil}}
\newenvironment{prf}{\underline{\textbf{Proof:}}}{\hfill$\openbox$}
\begin{document}
\begin{prf}
This is my proof using mathabx.
\end{prf}
\end{document}

I'd suggest you, however, to use the amsthm package and its built-in proof environment to typeset your proofs. This will give you, amongst other, proper spacing before and after the proofs, proper placement of the end-mark, no indentation for the first line.
In the follwoing example I used both environments for comparison (I suppressed the underlining, since it is not a typographical good practise, but you can add it back of you really need it):
\documentclass[11pt]{article}
\usepackage{amssymb}
\usepackage{mathabx}
\usepackage{amsthm}
\newenvironment{prf}{\underline{\textbf{Proof:}}}{\hfill$\openbox$}
\renewcommand\proofname{\normalfont\bfseries Proof:}
\begin{document}
\begin{prf}
This is my proof using mathabx.
\end{prf}
\begin{proof}
This is my proof using mathabx amnd amsthm.
\end{proof}
\end{document}

mathabx also offers \boxvoid, but this produces a square that it's slightly bigger than the regular \openbox command.
Are you sure you want to use mathabx? I ask you because the package redefines many math symbols (as you've already experienced). If you are interestef just in a particular symbol from mathabx, then Importing a Single Symbol From a Different Font shows you how to import the symbol without loading the package.