From longtable documentation:
Note however that \footnote will not work in the ‘head’ or ‘foot’
sections of the table. In order to put a footnote in those sections
(e.g., inside a caption), use \footnotemark at that point, and
\footnotetext anywhere in the table body that will fall on the same
page.
Hence the MWE will be
\documentclass{article}
\usepackage{longtable}
\begin{document}
\begin{longtable}{|c|}
\caption[Table is very long]{Table is very long\protect\footnotemark}\\ %<------footnote mark here
\hline
Something \footnotetext{This is a caption} \\ %<------footnote text here
\hline
\end{longtable}
\end{document}
Edit: Added short caption as per Gonzalo's suggestion. With short caption added, \protect won't be necessary.

\caption, as in\caption[Table is very long]{Table is very long\protect\footnotemark}to prevent the mark from having a wrong numbering in the text and from appearing also in a possible list of figures – Gonzalo Medina Mar 30 '12 at 23:52\protectis unnecessary. – Ivan Bychkov Apr 01 '12 at 21:50