Dependency Injection when using the Command Pattern

I'm using the Command Pattern for the first time. I'm a little unsure how I should handle dependencies.

In the code below, we dispatch a CreateProductCommand which is then queued to be executed at a later time. The command encapsulates all the information it needs to execute.

In this case it is likely we will need to access a data store of some type to create the product. My question is, how do I inject this dependency into the command so that it can execute?

public interface ICommand {
    void Execute();
}

public class CreateProductCommand : ICommand {
    private string productName;

    public CreateProductCommand(string productName) {
        this.ProductName = productName;
    }

    public void Execute() {
        // save product
    }
}

public class Dispatcher {
    public void Dispatch<TCommand>(TCommand command) where TCommand : ICommand {
        // save command to queue
    }
}

public class CommandInvoker {
    public void Run() {

        // get queue

        while (true) {
            var command = queue.Dequeue<ICommand>();
            command.Execute();
            Thread.Sleep(10000);
        }
    }
}

public class Client {
    public void CreateProduct(string productName) {
        var command = new CreateProductCommand(productName);
        var dispatcher = new Dispatcher();
        dispatcher.Dispatch(command);
    }
}

Many thanks
Ben