Recently we blocked the execution of Json schema pattern in Azure Logic Apps Parse Json action because of DoS security concerns. The matching XML XSD schema pattern feature however is available. Because of the per-customer sandbox environment in which the XML validation is executed for Logic Apps, we did not have to block use of XSD pattern. And Logic App supports converting Json to XML (native function xml()).
You may test this using the example XML schema and instance at: https://msdn.microsoft.com/en-us/library/ms256129(v=vs.110).aspx
Remember to associate the Logic App with an Integration Account (try the free SKU) prior to add the XML Validation action, as you will need the XML schema uploaded in the associated Integration Account.