I had further modified answer provided by Nicolas Herrera,because of security reason's we can't add plan text connection string to App service configuration section and on top of that, i was getting formatting issue for plan text connection string, so end up reading connection string value from key vault inside the configuration section
Connectionstring name = "your ConnectionString Key name"
Value = @Microsoft.KeyVault(SecretUri="your key vault uri")
Type = Custom ( it has to be custom , else it won't work) but again you can try diff type if you want to see what works for you
fyi i am still having connection string value in my config so that i can run my app locally for debugging purpose, connection string value is replaced per env, in App service as explained on microsoft documentation
For ASP.NET and ASP.NET Core developers, setting connection strings in App Service are like setting them in in Web.config, but the values you set in App Service override the ones in Web.config. You can keep development settings (for example, a database file) in Web.config and production secrets (for example, SQL Database credentials) safely in App Service. The same code uses your development settings when you debug locally, and it uses your production secrets when deployed to Azure.