see https://github.com/plotly/dash/issues/1056#issuecomment-997439760 or comment

dash_save_html.py

# -*- coding: utf-8 -*-
import os
from html.parser import HTMLParser

import dash
import pandas as pd
import plotly.express as px
import requests
from dash import html, dcc, dash_table, Input, Output


def patch_file(file_path: str, content: bytes, extra: dict = None) -> bytes:
    if file_path == 'index.html':
        index_html_content = content.decode('utf8')
        extra_jsons = f'''
        var patched_jsons_content={{
        {','.join(["'/" + k + "':" + v.decode("utf8") + "" for k, v in extra.items()])}
        }};
        '''
        patched_content = index_html_content.replace(
            '<footer>',
            f'''
            <footer>
            <script>
            ''' + extra_jsons + '''
            const origFetch = window.fetch;
            window.fetch = function () {
                const e = arguments[0]
                if (patched_jsons_content.hasOwnProperty(e)) {
                    return Promise.resolve({
                        json: () => Promise.resolve(patched_jsons_content[e]),
                        headers: new Headers({'content-type': 'application/json'}),
                        status: 200,
                    });
                } else {
                    return origFetch.apply(this, arguments)
                }
            }
            </script>
            '''
        ).replace(
            'href="/',
            'href="'
        ).replace(
            'src="/',
            'src="'
        )
        return patched_content.encode('utf8')
    else:
        return content


def write_file(file_path: str, content: bytes, target_dir='target', ):
    target_file_path = os.path.join(target_dir, file_path.lstrip('/').split('?')[0])
    target_leaf_dir = os.path.dirname(target_file_path)
    os.makedirs(target_leaf_dir, exist_ok=True)
    with open(target_file_path, 'wb') as f:
        f.write(content)
    pass


class ExternalResourceParser(HTMLParser):
    def __init__(self):
        super().__init__()
        self.resources = []

    def handle_starttag(self, tag, attrs):
        if tag == 'link':
            for k, v in attrs:
                if k == 'href':
                    self.resources.append(v)
        if tag == 'script':
            for k, v in attrs:
                if k == 'src':
                    self.resources.append(v)


def make_static(base_url, target_dir='target'):
    index_html_bytes = requests.get(base_url).content
    json_paths = ['_dash-layout', '_dash-dependencies', ]
    extra_json = {}
    for json_path in json_paths:
        json_content = requests.get(base_url + json_path).content
        extra_json[json_path] = json_content

    patched_bytes = patch_file('index.html', index_html_bytes, extra=extra_json)
    write_file('index.html', patched_bytes, target_dir)
    parser = ExternalResourceParser()
    parser.feed(patched_bytes.decode('utf8'))
    extra_js = [
        '_dash-component-suites/dash/dcc/async-graph.js',
        '_dash-component-suites/dash/dcc/async-plotlyjs.js',
        '_dash-component-suites/dash/dash_table/async-table.js',
        '_dash-component-suites/dash/dash_table/async-highlight.js'
    ]
    for resource_url in parser.resources + extra_js:
        resource_url_full = base_url + resource_url
        print(f'get {resource_url_full}')
        resource_bytes = requests.get(resource_url_full).content
        patched_bytes = patch_file(resource_url, resource_bytes)
        write_file(resource_url, patched_bytes, target_dir)


def main():
    port = 9050
    app = dash.Dash(__name__)
    df = pd.DataFrame({
        "Fruit": ["Apples", "Oranges", "Bananas", "Apples", "Oranges", "Bananas"],
        "Amount": [4, 1, 2, 2, 4, 5],
        "City": ["SF", "SF", "SF", "Montreal", "Montreal", "Montreal"]
    })

    fig = px.bar(df, x="Fruit", y="Amount", color="City", barmode="group")

    app.layout = html.Div(children=[
        html.Button('save static', id='save', n_clicks=0),
        html.Span('', id='saved'),

        html.H1(children='Hello Dash'),

        html.Div(children='''
            Dash: A web application framework for your data.
        '''),

        dcc.Graph(
            id='example-graph',
            figure=fig
        ),
        dash_table.DataTable(
            id='table',
            columns=[{"name": i, "id": i} for i in df.columns],
            data=df.to_dict('records'),
        )
    ])

    @app.callback(
        Output('saved', 'children'),
        Input('save', 'n_clicks'),
    )
    def save_result(n_clicks):
        if n_clicks == 0:
            return 'not saved'
        else:
            make_static(f'http://127.0.0.1:{port}/')
            return 'saved'

    app.run_server(debug=False, port=port)


if __name__ == '__main__':
    main()

Hi. Very nice snippet!!!
For those encountering the issue mentioned by @RajonDawn, just change these:
extra_js = [
"_dash-component-suites/dash/dcc/async-graph.js",
# "_dash-component-suites/dash/dcc/async-plotlyjs.js", # TODO: remove
"_dash-component-suites/dash/dash_table/async-table.js",
"_dash-component-suites/dash/dash_table/async-highlight.js",
"_dash-component-suites/plotly/package_data/plotly.min.js", # TODO: add
]