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.onComplete = onDismiss;
    }
    
    void Start()
    {
        StartCoroutine("Do");
    }

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

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.

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.