Azure Functions Python will have PYODBC module installed by default. Make sure to add pyodbc in requirements.txt.

I used the below code to connect and query Select statement with Azure SQL using Azure Functions and it worked successfully, Refer below:-

My init.py:-

import logging
from multiprocessing import connection
import pyodbc
import os
import azure.functions as func

def main(req: func.HttpRequest) -> func.HttpResponse:
    logging.info('Python HTTP trigger function processed a request.')
    
    connectionstring = os.environ["connectionstring"]
    conn = pyodbc.connect(connectionstring)
    cursor = conn.cursor()
  
    cursor.execute("SELECT * FROM StudentReviews")
    conn.commit()
    
    conn.commit()
    cursor.close()
    conn.close()

        
    # Prepare & Return the HTTP Response
    return func.HttpResponse(
                body="Your request is processed",
                status_code=202
        )

requirements.txt:-

azure-functions
pyodbc

local.settings.json:-

{
  "IsEncrypted": false,
  "Values": {
    "AzureWebJobsStorage": "DefaultEndpointsProtocol=https;AccountName=siliconrg8c29;AccountKey=xxxxxxxxxqvo9mCwMuHlTpFk5yzn/Wk/bu3Wy1rxlxxxxx==;EndpointSuffix=core.windows.net",
    "FUNCTIONS_WORKER_RUNTIME": "python",
    "connectionstring" : "DRIVER={ODBC Driver 17 for SQL Server};SERVER=tcp:sqlserver.database.windows.net;PORT=1433;DATABASE=silicondb;UID=username;PWD=Password"
  }
}

I deployed the above function code in my Azure Function app created with Runtime set to Python 3.10 and Linux OS like below:-

Commands to deploy the Function:-

az login
az account set --subscription "SID Subscription"
func azure functionapp publish siliconfunc430

Added connectionstring setting in the configuration as settings from local.settings.json is not added in the Function app while deployment.

Make sure you check the Function Outbound Ip's and whitelist these Ip's in your SQL as mentioned in this SO thread answer.

One alternative is to deploy your Function app in a dedicated plan, Either Premium plan or App Service plan and then run the commands from this Document to install ODBC Driver manually in your Function app.

Commands:-

Checked the OS version that was Debian and than ran the script from the document specific to Debian.

cat /etc/os-release

sudo su curl https://packages.microsoft.com/keys/microsoft.asc |
apt-key add -

#Download appropriate package for the OS version
#Choose only ONE of the following, corresponding to your OS version

#Debian 9 curl https://packages.microsoft.com/config/debian/9/prod.list >
/etc/apt/sources.list.d/mssql-release.list

#Debian 10 curl https://packages.microsoft.com/config/debian/10/prod.list >
/etc/apt/sources.list.d/mssql-release.list

#Debian 11 curl https://packages.microsoft.com/config/debian/11/prod.list >
/etc/apt/sources.list.d/mssql-release.list

exit sudo apt-get update sudo ACCEPT_EULA=Y apt-get install -y
msodbcsql17
# optional: for bcp and sqlcmd sudo ACCEPT_EULA=Y apt-get install -y mssql-tools echo 'export PATH="$PATH:/opt/mssql-tools/bin"' >>
~/.bashrc source ~/.bashrc
# optional: for unixODBC development headers sudo apt-get install -y unixodbc-dev
# optional: kerberos library for debian-slim distributions sudo apt-get install -y libgssapi-krb5-2