There is no function provided by default, but you can do the following by using Streams (if your String has exactly that format you specified):
String[][] a = 
    Arrays.stream(s.substring(2, s.length()-2).split("\\],\\["))
        .map(sub -> sub.split(","))
        .toArray(String[][]::new);
Here, you cut off the first and last two brackets (.substring(2, s.length()-2)), then split your String (.split("\\],\\["))(which results in an array of Strings of format "asdf,fdsa".
Array.stream creates a stream of that, map splits those Strings to arrays, and then you can collect them with the toArray-method.
Printing this array of arrays leads to:
1509321600000   35166.44    
1509408000000   35224.31    
1509580800000   35234.60