Hi nadeem1218,
Refer the below sample.
HTML
<%@ Register Assembly="AjaxControlToolkit" Namespace="AjaxControlToolkit" TagPrefix="cc1" %>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
        .modalBackground
        {
            background-color: Black;
            filter: alpha(opacity=60);
            opacity: 0.6;
        }
        .modalPopup
        {
            background-color: #FFFFFF;
            width: 500px;
            border: 3px solid #0DA9D0;
            padding: 0;
        }
        .modalPopup .header
        {
            background-color: #2FBDF1;
            height: 30px;
            color: White;
            line-height: 30px;
            text-align: center;
            font-weight: bold;
        }
        .modalPopup .body
        {
            min-height: 50px;
            padding: 5px;
            line-height: 30px;
            text-align: center;
            font-weight: bold;
        }
    </style>
</head>
<body>
    <form id="form1" runat="server">
    <cc1:ToolkitScriptManager ID="ToolkitScriptManager1" runat="server">
    </cc1:ToolkitScriptManager>
    <asp:TextBox ID="txtUrl" runat="server" Width="300" Text="https://www.youtube.com/watch?v=cWuvnc6u93A" />
    <asp:Button ID="btnShow" runat="server" Text="Play Video" OnClick="Play" />
    <asp:LinkButton ID="lnkDummy" runat="server"></asp:LinkButton>
    <cc1:ModalPopupExtender ID="ModalPopupExtender1" BehaviorID="mpe" runat="server"
        PopupControlID="pnlPopup" TargetControlID="lnkDummy" BackgroundCssClass="modalBackground"
        CancelControlID="btnClose">
    </cc1:ModalPopupExtender>
    <asp:Panel ID="pnlPopup" runat="server" CssClass="modalPopup" Style="display: none">
        <div class="header">
            Youtube Video
        </div>
        <div class="body">
            <iframe id="video" runat="server" width="420" height="315" frameborder="0" allowfullscreen>
            </iframe>
            <br />
            <br />
            <asp:Button ID="btnClose" runat="server" Text="Close" />
        </div>
    </asp:Panel>
    </form>
</body>
</html>
C#
protected void Play(object sender, EventArgs e)
{
    string[] separatingChars = { "v=" };
    string url = "//www.youtube.com/embed/" + txtUrl.Text.Split(separatingChars, StringSplitOptions.RemoveEmptyEntries)[1];
    video.Attributes["src"] = url;
    ModalPopupExtender1.Show();
}
VB.Net
Protected Sub Play(sender As Object, e As EventArgs)
    Dim separatingChars As String() = {"v="}
    Dim url As String = "//www.youtube.com/embed/" + txtUrl.Text.Split(separatingChars, StringSplitOptions.RemoveEmptyEntries)(1)
    video.Attributes("src") = url
    ModalPopupExtender1.Show()
End Sub
Screenshot

