You can do it by simply writing its Display Property to NONE. For REference you can see the code provided below..
<asp:textbox id="txtWebSite1" runat="server" xmlns:asp="#unknown"></asp:textbox>
<asp:requiredfieldvalidator id="RequiredFieldValidator10" runat="server" controltovalidate="txtWebSite1" validationgroup="popup" display="None" errormessage="Website is Required." xmlns:asp="#unknown">
</asp:requiredfieldvalidator>
Here, you can see i have provided
Display="None" so that it will not going to be displayed besides text box. but it will show in the <asp:validationsummary xmlns:asp="#unknown"> block.
Have a Nice DAY.....