How inject service in AutoMapper profile class

To solve your problem you just need to wire IUserManager in DI, and make sure UserProfile dependency is resolved.

public void ConfigureServices(IServiceCollection services)
{
    // ...
    services.AddSingleton<IUserManager, UserManager>();
    services.AddSingleton(provider => new MapperConfiguration(cfg =>
    {
        cfg.AddProfile(new UserProfile(provider.GetService<IUserManager>()));
    }).CreateMapper());
}

And having that said, I would probably try to keep single responsibility per class, and not have any services injected into mapping profiles. You can populate your objects just before the mapping instead. This way it might be easier to unit test as well.