You should be able to use non-greedy quantifiers, specifically *?. You’re going to probably want the following:
Pattern MY_PATTERN = Pattern.compile("\\[(.*?)\\]");
This will give you a pattern that will match your string and put the text within the square brackets in the first group. Have a look at the Pattern API Documentation for more information.
To extract the string, you could use something like the following:
Matcher m = MY_PATTERN.matcher("FOO[BAR]");
while (m.find()) {
String s = m.group(1);
// s now contains "BAR"
}