Just got a solution from Kentico Support team via email, Thanks!
The solution is below:

In .ascx:
<div class="Calendar">
<cms:CMSCalendar ID="calItems" runat="server" OnVisibleMonthChanged="calItems_VisibleMonthChanged">
</cms:CMSCalendar>
<asp:Literal ID="evtListHeading" runat="server"></asp:Literal>
<cms:CMSRepeater ID="repEvtList" runat="server">
</cms:CMSRepeater>
</div>

In ascx.cs:
protected void calItems_VisibleMonthChanged(object sender, MonthChangedEventArgs e)
{
this.evtListHeading.Text = "<div class=\"EvtListHeading\">" + e.NewDate.ToString("MMMM yyyy") + " Events</div>";

DateTime BeginDt = new DateTime(e.NewDate.Year, e.NewDate.Month, 1);
DateTime EndDt = BeginDt.AddMonths(1);

this.repEvtList.WhereCondition = "EventDate between '" + BeginDt.Date.ToString() + "' and '" + EndDt.Date.ToString() + "'";
this.repEvtList.ReloadData(true);

}