If you use .Net 4.5 you can also use standard .Net json serializer:
using System.Runtime.Serialization.Json;
...
Stream jsonSource = ...; // serializer will read data stream
var s = new DataContractJsonSerializer(typeof(string[][]));
var j = (string[][])s.ReadObject(jsonSource);
In .Net 4.5 and older you can use JavaScriptSerializer class:
using System.Web.Script.Serialization;
...
JavaScriptSerializer serializer = new JavaScriptSerializer();
string[][] list = serializer.Deserialize<string[][]>(json);