In general: hyperref loads package url in background. So to change the font the right command is \urlstyle{…} (default is tt for teletype, i.e. \ttfamily), cf. manual of url.
Since you did not provide a minimal working example (MWE) I suppose you used the truetype font Euclid Regular (a free font), which has to be set with fontspec, and the TeX file must be compiled with LuaLaTeX or XeLaTeX.
\documentclass{article}
\usepackage{fontspec}
\setmainfont{euclid.ttf} % if properly installed "\setmainfont{Euclid}" is preferred
\usepackage{kantlipsum} % just for some dummy text
\usepackage{hyperref} % loads "url" in background
\setlength{\parindent}{0pt} % for the example
\begin{document}
\kant[50]
\bigskip
\url{http://stackoverflow.com/} -- \url{http://tex.stackexchange.com/questions/162164/}
\urlstyle{rm}
\url{http://stackoverflow.com/} -- \url{http://tex.stackexchange.com/questions/162164/}
\bigskip
\kant[51]
\end{document}
Because for the test I did not install euclid.ttf in the fonts folder of my system I had to give the filename in \setmainfont instead of the preferred fontname (Euclid).
\documentclass{...}and ending with\end{document}. – Speravir Feb 24 '14 at 20:39\urlstyle{rm}in your document preamble (after having loadedhyperref). – egreg Feb 24 '14 at 21:50