Update from January 2023.

XlsxWriter 3.0.6+ now supports a autofit() worksheet method:

from xlsxwriter.workbook import Workbook

workbook = Workbook('autofit.xlsx')
worksheet = workbook.add_worksheet()

# Write some worksheet data to demonstrate autofitting.
worksheet.write(0, 0, "Foo")
worksheet.write(1, 0, "Food")
worksheet.write(2, 0, "Foody")
worksheet.write(3, 0, "Froody")

worksheet.write(0, 1, 12345)
worksheet.write(1, 1, 12345678)
worksheet.write(2, 1, 12345)

worksheet.write(0, 2, "Some longer text")

worksheet.write(0, 3, "http://ww.google.com")
worksheet.write(1, 3, "https://github.com")

# Autofit the worksheet.
worksheet.autofit()

workbook.close()

Output:

Or using Pandas:

import pandas as pd

# Create a Pandas dataframe from some data.
df = pd.DataFrame({
    'Country':    ['China',    'India',    'United States', 'Indonesia'],
    'Population': [1404338840, 1366938189, 330267887,       269603400],
    'Rank':       [1,          2,          3,               4]})

# Order the columns if necessary.
df = df[['Rank', 'Country', 'Population']]

# Create a Pandas Excel writer using XlsxWriter as the engine.
writer = pd.ExcelWriter('pandas_autofit.xlsx', engine='xlsxwriter')
df.to_excel(writer, sheet_name='Sheet1', index=False)

# Get the xlsxwriter workbook and worksheet objects.
workbook = writer.book
worksheet = writer.sheets['Sheet1']

worksheet.autofit()

# Close the Pandas Excel writer and output the Excel file.
writer.close()

Output: