Change the value of \separatorcolumnwidth
to the value you need.
See for example the code (see marked code with <
=======`):
\documentclass[11pt,a4paper,sans]{moderncv}
\moderncvstyle{classic}
\usepackage{graphicx}
\firstname{John}
\familyname{Doe}
\address{83 Fancy Avenue}{Noweheresville}{Gotham City 24061}
\phone[mobile]{123 456 7890}
\email{someone@xyz.com}
\photo[64pt][0.5pt]{example-image-a}
\setlength{\separatorcolumnwidth}{0mm} % <==============================
\begin{document}
\makecvtitle
\end{document}
and its result:

To get the usual distance back after the title just use \setlength
again:
\documentclass[11pt,a4paper,sans]{moderncv}
\moderncvstyle{classic}
\usepackage{graphicx}
\firstname{John}
\familyname{Doe}
\address{83 Fancy Avenue}{Noweheresville}{Gotham City 24061}
\phone[mobile]{123 456 7890}
\email{someone@xyz.com}
\photo[64pt][0.5pt]{example-image-a}
\setlength{\separatorcolumnwidth}{0mm} % <==============================
\begin{document}
\makecvtitle
\setlength{\separatorcolumnwidth}{9pt}% <===============================
\section{Education}
\cventry{year--year}{Degree}{Institution--3}{City--4}{\textit{Grade}--5}{Description--6} % arguments 3 to 6 can be left empty
\cventry{year--year}{Degree}{Institution}{City}{\textit{Grade}}{Description}
\section{Master thesis}
\cvitem{title}{\emph{Title}}
\cvitem{supervisors}{Supervisors}
\cvitem{description}{Short thesis abstract}
\end{document}
and the result:
