When you interpolate a variable in a regular expression, regex metacharacters are evaluated as if you'd used them in the regex. So, in your example, the '.' character is evaluated as matching 'any character'. You can either escape the regex metacharacters in the word you're searching for or use the \Q\E pair to automatically quote metacharacters, such as:

/\Q$word/E/ or /\Q$word/

(The \E can actually be omitted, it's there so that you can enclose a subset of the regex)