"Woman's Day you are a disgrace," he wrote on his Instagram page.
"I'm not sure what possess you to continue this attack & making up lies about me, my family or my private life. What is the media watchdog doing about this constant harassment & continual lies about made up stories with no substance whatsoever?"
Callahan also slammed the reports, telling Daily Mail Australia: '[It's a] completely made-up [story]. I'm not worried at all. He's a great normal kid and is just having fun with his dad.'
'Completely made-up, Jackson has been playing poker since Shane taught him when he was about five-years-old, all the kids love it, we all played games,' Simone told Daily Mail Australia on Monday.
'This year Jackson was 18 and it's a great opportunity for them to play at [Melbourne's] Crown in the Aussie Millions [Poker Championship] together. I'm not worried at all.'
Simone married Shane in 1995, later calling it quits in 2005.
The high-profile pair briefly reunited in April 2007 before splitting just months later in September.
In an interview with New Idea, Simone previously claimed that she had broken things off because Shane had sent her a text message meant for another woman.
'I'm absolutely devastated but it was the wake-up call I needed. I'd been very suspicious for some time that he was up to his old tricks,' she said at the time.
Shane denied he had an affair and said he had sent the SMS after he and Simone had split.
Since parting ways with the cricketer, Simone has dated Toby Roberts, however, the pair split in 2012 after 18 months together.
While no longer a couple, Simone and Shane have remained committed to co-parenting their three children.