He wrote: "Bantz aside, I hope you guys can resolve your situation or this is a hack as we have never even met! Plus I like my women BBW #ItWasntMe".
Mr Khan's Twitter account has previously been targeted by hackers, as has that of his New York-born wife.
As social media users rubbed their hands with glee as they followed the escalating row, messages posted to Mrs Khan's Twitter account also hit back at the claims.
Mr Khan apparently wrote: "'Left my family and friends for this Faryal. I'm not hurt but another fighter. I'm making it public. You getting the divorce #Golddigger"
Minutes later his wife's account responded, telling him: "Stop making false things up".
Tweets later deleted continued: "After all these years. I've always defending a cheat, always stuck around for him, always had his back. And I'm called a gold digger?"
"The amount of evidence I have on you. It can destroy you. But since I loved you at one point in my life. I'll just let it go."
Retweeting the allegations surrounding Mr Joshua it was added: "You have actually lost it. Wtf. where do u make this stuff up from?".
Mrs Khan apparently added: "I think he just needs some attention because boxing hasn't been going well for him so he's just been acting up. #30yearoldbaby.
"Sometimes people don't like it when you give them a taste of their own medicine."
Amid an increasingly trend for people to air their dirty laundry online, it is not the first time that the couple's private lives have been played out in a very public sphere.
Makdhoom and Khan's family have indulged in Twitter arguments in the last year, with Khan having standing behind his wife.
The disagreements began when she came to blows with his family over her choice of clothing and her faith.
In a TV interview Mrs Khan, who once posted a naked picture of her brother-in-law online, claimed that "it's not in my nature to ever go public about personal matters" but said she had endured bullying and was called a gold digger.
Her parents later revealed their fears that their son-in-law would divorce Makhdoom following the protracted war of words between the family.
The couple had married in a high-profile New York wedding on 31 May 2013 at the Waldorf Astoria, the boxer having become engaged to the Pakistani-American student, from Staten Island, in January 2012.
They then flew back to Khan's hometown of Bolton where a second celebration, a traditional Walima, took place in Manchester, which included 4,000 guests.
Their first child, a daughter named Lamaisah, was born on 23 May 2014.
As of July 2013, Khan's net worth was £23 million ($31 million). In 2014, he earned $15 million that year, making him the sixth highest-earning boxer of 2014.
Neither of them responded to a request for comment.
