TIMTOWTDI, albeit, a less than entirely satisfactory way, requiring another step beyond what's here:

#!/usr/bin/perl
use Modern::Perl;
use Data::Dumper;
# 947251

my $string = '1945,"4,399.00",938,1/10/2012';

my @string = split /(,".*?(?=")?")/, $string;
print Dumper @string;

=head output

$VAR1 = '1945';
$VAR2 = ',"4,399.00"';  # note the leading commas retained and must be
+ reprocessed
$VAR3 = ',938,1/10/2012'; # see 

=cut
[download]

See the examples in split beginning at "If the PATTERN contains parentheses, additional list elements ...."