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Unity doesn’t really support modal dialogs in the way you want, but there are some workaround, like setting the time scale to zero while it’s displayed, and adding a click-blocking later between the message box and everything underneath it.

There are also better ways to wait for the message box to be dismissed than a coroutine, such as a UnityEvent.

That said, if you just want to move your coroutine into the MessageBox class, it should be pretty simple: (warning: untested)

public class MessageBox : MonoBehaviour 
{
    private System.Action onDismiss;
    public static void ShowMessage(string msg, System.Action onDismiss)
    {
        GameObject obj = (GameObject)Instantiate(Resources.Load("MsgBox"));

        obj.GetComponentInChildren<Text>().text = msg;
        MessageBox msg = obj.AddComponent<MessageBox>(); //or this component could be added to the prefab in the inspector.
        msg.onDismiss = onDismiss;
    }
    
    void Start()
    {
        StartCoroutine("Do");
    }

    IEnumerator Do()
    {
        yield return new WaitUntil(() => GlobalVariables.MsgBoxClicked);
        //GlobalVariables is a separate class containing some static variables.
        if (onDismiss != null)
            onDismiss();
    }
}

And then the code that wants to show the message can simply use

MessageBox.ShowMessage("This is a test message!", () => {
    Debug.Log("Done!");
});

Basically, MonoBehaviour objects can’t exist on their own. They are components that must be attached to a GameObject, which is what the call to AddComponent is doing.