\documentclass[12pt]{article}
\usepackage{cmap}
\usepackage[T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[format=plain,
justification=raggedright,singlelinecheck=false]{caption}
\usepackage[russian]{babel}
\begin{document}
\begin{figure}
\caption{\label{my-fig} Русский текст подписи. \\ Fig. \ref{my-fig}: English text.}
\end{figure}
\end{document}