Voici la solution de RameshVel traduite en java :
DB db = conn.getDB( "yourDB" );
DBCollection coll = db.getCollection( "yourCollection" );
ObjectId _id = new ObjectId("4e71b07ff391f2b283be2f95");
ObjectId arrayId = new ObjectId("4e639a918dca838d4575979c");
BasicDBObject query = new BasicDBObject();
query.put("_id", _id);
query.put("array._arrayId", arrayId);
BasicDBObject data = new BasicDBObject();
data.put("array.$.someField", "updated");
BasicDBObject command = new BasicDBObject();
command.put("$set", data);
coll.update(query, command);