Hi,
You need to create validationGroup for given code.
Update your code like,
<asp:textbox id="TextBox1" runat="server" validationgroup="group" readonly="True" xmlns:asp="#unknown"></asp:textbox>
<asp:button id="Button1" runat="server" text="Button" validationgroup="group" onclick="Button1_Click" xmlns:asp="#unknown" />
Hope this helps you,
Thanks
-Amit Gajjar