ashraft1 says:

google.load("visualization", "1", { packages: ["corechart"] });

    google.setOnLoadCallback(function () {

        drawChart();

        $("#DrpMonth").on("change", function () {

            drawChart();

        });

    });

Change the above with the below code.

google.load("visualization", "1", { packages: ["corechart"] });
google.setOnLoadCallback(function () {
    $("#DrpMonth").on("change", function () {
        drawChart();
    });
});

Refering the below article i have created an example.

Google Chart APIs: Google (Pie / Doughnut) Chart example with database in ASP.Net

Check this example. Now please take its reference and correct your code.

HTML

<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript" src="https://www.google.com/jsapi"></script>
<script type="text/javascript">
    google.load("visualization", "1", { packages: ["corechart"] });
    google.setOnLoadCallback(function () {
        // Draw Chart on DropDownList change.
        $("[id*=DrpMonth]").on("change", function () {
            drawChart();
        });
        // Draw Chart on Button click.
        $("[id*=btnShowChart]").on("click", function () {
            drawChart();
            return false;
        });
    });
    function drawChart() {
        var country = $("[id*=DrpMonth] option:selected").val();
        $.ajax({
            type: "POST",
            url: "Default.aspx/GetChartData",
            data: "{country: '" + country + "'}",
            contentType: "application/json; charset=utf-8",
            dataType: "json",
            success: function (r) {
                var data = google.visualization.arrayToDataTable(r.d);
                var chart = new google.visualization.PieChart($("#chart")[0]);
                chart.draw(data, { title: country + ' Distribution', is3D: false });
            },
            failure: function (r) {
                alert(r.d);
            },
            error: function (r) {
                alert(r.d);
            }
        });
    }
</script>
<center>
    <asp:DropDownList ID="DrpMonth" runat="server">
        <asp:ListItem Text="Select" Value="Select" Selected="True"></asp:ListItem>
        <asp:ListItem Text="Finland" Value="Finland"></asp:ListItem>
        <asp:ListItem Text="Brazil" Value="Brazil"></asp:ListItem>
        <asp:ListItem Text="USA" Value="USA"></asp:ListItem>
        <asp:ListItem Text="Italy" Value="Italy"></asp:ListItem>
        <asp:ListItem Text="Germany" Value="Germany"></asp:ListItem>
    </asp:DropDownList>
    <asp:Button ID="btnShowChart" Text="Show Chart" runat="server" />
</center>
<div id="chart" style="width: 900px; height: 500px;">
</div>

Namespace

C#

using System.Data;
using System.Web.Services;
using System.Configuration;
using System.Data.SqlClient;

VB.Net

Imports System.Data
Imports System.Web.Services
Imports System.Configuration
Imports System.Data.SqlClient

Code

C#

[WebMethod]
public static List<object> GetChartData(string country)
{
    string query = "SELECT ShipCity, COUNT(orderid) TotalOrders FROM Orders WHERE ShipCountry = @Country GROUP BY ShipCity";
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    List<object> chartData = new List<object>();
    chartData.Add(new object[] { "ShipCity", "TotalOrders" });
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query))
        {
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            cmd.Parameters.AddWithValue("@Country", country);
            con.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    chartData.Add(new object[] { sdr["ShipCity"], sdr["TotalOrders"] });
                }
            }
            con.Close();
            return chartData;
        }
    }
}

VB.Net

<WebMethod()>
Public Shared Function GetChartData(ByVal country As String) As List(Of Object)
    Dim query As String = "SELECT ShipCity, COUNT(orderid) TotalOrders FROM Orders WHERE ShipCountry = @Country GROUP BY ShipCity"
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Dim chartData As List(Of Object) = New List(Of Object)()
    chartData.Add(New Object() {"ShipCity", "TotalOrders"})
    Using con As SqlConnection = New SqlConnection(constr)
        Using cmd As SqlCommand = New SqlCommand(query)
            cmd.CommandType = CommandType.Text
            cmd.Connection = con
            cmd.Parameters.AddWithValue("@Country", country)
            con.Open()
            Using sdr As SqlDataReader = cmd.ExecuteReader()
                While sdr.Read()
                    chartData.Add(New Object() {sdr("ShipCity"), sdr("TotalOrders")})
                End While
            End Using

            con.Close()
            Return chartData
        End Using
    End Using
End Function