Is it possible to read data from an Excel sheet in Python using Xlsxwriter? If so how?

It is not possible to read data from an Excel file using XlsxWriter.

There are some alternatives listed in the documentation.

If you want to use xlsxwriter for manipulating formats and formula that you can't do with pandas, you can at least import your excel file into an xlsxwriter object using pandas. Here's how.

import pandas as pd
import xlsxwriter   

def xlsx_to_workbook(xlsx_in_file_url, xlsx_out_file_url, sheetname):
    """
    Read EXCEL file into xlsxwriter workbook worksheet
    """
    workbook = xlsxwriter.Workbook(xlsx_out_file_url)
    worksheet = workbook.add_worksheet(sheetname)
    #read my_excel into a pandas DataFrame
    df = pd.read_excel(xlsx_in_file_url)
    # A list of column headers
    list_of_columns = df.columns.values

    for col in range(len(list_of_columns)):
        #write column headers.
        #if you don't have column headers remove the folling line and use "row" rather than "row+1" in the if/else statments below
        worksheet.write(0, col, list_of_columns[col] )
        for row in range (len(df)):
            #Test for Nan, otherwise worksheet.write throws it.
            if df[list_of_columns[col]][row] != df[list_of_columns[col]][row]:
                worksheet.write(row+1, col, "")
            else:
                worksheet.write(row+1, col, df[list_of_columns[col]][row])
    return workbook, worksheet

# Create a workbook
#read you Excel file into a workbook/worksheet object to be manipulated with xlsxwriter
#this assumes that the EXCEL file has column headers
workbook, worksheet = xlsx_to_workbook("my_excel.xlsx", "my_future_excel.xlsx", "My Sheet Name")

###########################################################
#Do all your fancy formatting and formula manipulation here
###########################################################

#write/close the file my_new_excel.xlsx
workbook.close()