I am working on an ASP.NET application that uses the AspNetSqlMembershipProvider for the authentication mechanism.
I am transferring the application to a cloud application in order to deploy it on windows azure.
Do I have to change the authentication mechanism that I use or will the AspNetSqlMembershipProvider will work normally?
You have no need to change the Authentication Mechanism for the reason of deployment. Just make the local machine database scripts to run on the sql azure database. Everything should be work same as you are doing authentication on local development machine.
Check these links to know regarding this deployment of sql authentication or database script etc:
Trying to deploy Asp.Net Memebership database to SQL Azure
Updated ASP.net scripts for use with Microsoft SQL Azure
After installing the scripts, just change the connection string in the webconfig that provide the authentication through database.