You'll want to use placeholder variables instead, that will take care of the quoting for you.

my $sql_fmt = "INSERT INTO whatever VALUES(?,?,?,?,?,?,?,?,?,?,?,?,?,?
+)"; 
 while (<INFILE>)   {
     my @line = (parse_csv ($_)); 
     $dbh->do($sql_fmt,undef,@line);
 }
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You just need to make sure you always have the same number of array elements in @line that you have '?' marks in $sql_fmt or DBI will give you an error.

Also it's a good idea to format your SQL statements like: INSERT INTO whatever (column_names) VALUES(?...) That way all your insert statements won't break if you decide to add to your database structure.