This message was posted on behalf of Intel Corporation
The Ethernet shield is not included in the Shield Testing Report for Intel® Galileo and Edison Boards (http://www.intel.com/content/dam/support/us/en/documents/Galileo-Edison_ShieldTestReport_330937-002.pdf). So, it is not validated to work with Edison.
However, there's a guide about how to connect Edison using Ethernet over USB (https://software.intel.com/en-us/connecting-to-intel-edison-board-using-ethernet-over-usb). Maybe it'll be of help for you.