A re-implementation of Adam's kivy widget (https://stackoverflow.com/users/1281548/adam) (https://stackoverflow.com/questions/13714074/kivy-date-picker-widget#) in Material Design using KivyMD

datepicker.py

from kivy.event import EventDispatcher
from kivy.metrics import dp
from kivy.properties import ListProperty, StringProperty
from kivymd.uix.behaviors import FakeRectangularElevationBehavior
from kivymd.uix.card import MDCard
from kivy.uix.behaviors import ToggleButtonBehavior

from kivy.uix.gridlayout import GridLayout
from kivy.uix.boxlayout import BoxLayout
from kivy.uix.label import Label
from kivymd.uix.button import MDRaisedButton

from kivymd.app import MDApp

from datetime import date, timedelta
from kivy.lang import Builder

Builder.load_string("""
<DateButton>:
    elevation: .1
    radius: dp(10)
    ripple_behavior: True
    Label:
        text: root.text
        color: root.text_color

""")


class DateButton(MDCard, FakeRectangularElevationBehavior, ToggleButtonBehavior):
    text_color = ListProperty([0, 0, 0, .6])
    text = StringProperty("")

    def on_state(self, widget, value):
        if value == 'down':
            self.md_bg_color = self.theme_cls.primary_color
            self.text_color = [1, 1, 1, 1]
        else:
            self.md_bg_color = [1, 1, 1, 1]
            self.text_color = [0, 0, 0, .6]


class DatePicker(BoxLayout, EventDispatcher):
    # butt

    def __init__(self, *args, **kwargs):
        super(DatePicker, self).__init__(**kwargs)
        self.register_event_type("on_select")
        self.date = date.today()
        self.days = (
            "Mon",
            "Tue",
            "Wed",
            "Thur",
            "Fri",
            "Sat",
            "Sun"
        )
        self.orientation = "vertical"
        self.month_names = (
            'January',
            'February',
            'March',
            'April',
            'May',
            'June',
            'July',
            'August',
            'September',
            'October',
            'November',
            'December'
        )
        if "month_names" in kwargs:
            self.month_names = kwargs['month_names']
        self.header = BoxLayout(orientation='horizontal',
                                size_hint=(1, 0.2))
        self.body = GridLayout(cols=7, spacing=dp(20))
        self.add_widget(self.header)
        self.add_widget(self.body)

        self.populate_body()
        self.populate_header()

    def populate_header(self, *args, **kwargs):
        self.header.clear_widgets()
        previous_month = MDRaisedButton(text="<", pos_hint={"center_y": .5}, on_release=self.move_previous_month)
        previous_month.bind()
        next_month = MDRaisedButton(text=">", on_release=self.move_next_month, pos_hint={"center_y": .5})
        month_year_text = self.month_names[self.date.month - 1] + ' ' + str(self.date.year)
        current_month = Label(text=month_year_text, size_hint=(2, 1), color=[0, 0, 0, .6])

        self.header.add_widget(previous_month)
        self.header.add_widget(current_month)
        self.header.add_widget(next_month)

    def populate_body(self, *args, **kwargs):
        self.body.clear_widgets()
        date_cursor = date(self.date.year, self.date.month, 1)
        for day in self.days:
            self.body.add_widget(Label(text=day, color=[0, 0, 0, .5]))
        for filler in range(date_cursor.isoweekday() - 1):
            self.body.add_widget(Label(text=""))
        while date_cursor.month == self.date.month:
            date_label = DateButton(text=str(date_cursor.day), group="date")
            date_label.bind(
                on_release=lambda x, _date=int(date_label.text): self.set_date(
                    day=date(self.date.year, self.date.month, _date)
                )
            )
            if self.date.day == date_cursor.day:
                date_label.state = "down"
            self.body.add_widget(date_label)
            date_cursor += timedelta(days=1)

    def set_date(self, day):
        self.date = day
        self.dispatch("on_select", day)

    def on_select(self, day):
        pass

    def move_next_month(self, *args, **kwargs):
        if self.date.month == 12:
            self.date = date(self.date.year + 1, 1, self.date.day)
        else:
            self.date = date(self.date.year, self.date.month + 1, self.date.day)
        self.populate_header()
        self.populate_body()

    def move_previous_month(self, *args, **kwargs):
        if self.date.month == 1:
            self.date = date(self.date.year - 1, 12, self.date.day)
        else:
            self.date = date(self.date.year, self.date.month - 1, self.date.day)
        self.populate_header()
        self.populate_body()


class MyApp(MDApp):

    def build(self):
        box = BoxLayout(padding=dp(20))
        box.add_widget(DatePicker())
        return box


if __name__ == '__main__':
    MyApp().run()