The accusation was aimed at Haraldur Thorleifsson, a former Twitter director who engaged in a public spat with Musk on Monday.
Musk tweeted: "The reality is that this guy (who is independently wealthy) did no actual work, claimed as his excuse that he had a disability that prevented him from typing, yet was simultaneously tweeting up a storm. Can't say I have a lot of respect for that."
Musk added: "But was he fired? No, you can't be fired if you weren't working in the first place!"
A statement on Thorleifsson's personal website, posted before his altercation with Musk, says: "I have genetic muscle atrophy, often called muscle dystrophy. The one I have is called Dysferlinopathy. I use a wheelchair and I am slowly but surely losing strength in my upper body and arms. I don't like it but that doesn't really change anything."
Twitter and Thorleifsson didn't immediately respond to Insider's requests for comment.
Amid his spat with Musk on Monday, Thorleifsson posted a picture of himself in a wheelchair. He later posted a Twitter thread describing the effects of muscular dystrophy on his body.
Thorleifsson said later he'd received an email from Twitter's head of HR, who confirmed he was no longer employed by the company.
Disabled employees at Twitter filed a class-action lawsuit against the company in November, saying Musk's new "extremely hardcore" work culture and orders to "work long hours at high intensity" forced them to resign.
