I'd use * instead of +, since he didn't say empty fields were not allowed. And what if the bracket are is not the first character? Fixed and documented:

$_ = "abc,xyz,{1,2,3,4},18-90-89,{{1,2},{5,6,7,8}},yts";


# Create a regexp to match nested brackets.

my $par;  # Can't combine this with next line.

$par = qr/ \{             # Opening bracket.
          (?:             # Match zero or more
             [^{}]+       #    non-brackets
             |            #    or
             (??{ $par }) #    bracketed content.
           )*
           \}             # Closing bracket.
       /x;


# Extract fields from the line.

my @elems = / \G                 # Start where last match left off.
              (                  # Capture (return)
                 (?:             #    zero or more
                    [^{,]+       #       non-brackets, non-commas
                    |            #       or
                    $par         #       bracketed content.
                 )*
              )
              (?: , | $)         # Match comma or end of line.
            /xg;


print(join("\n", @elems));
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