Apple shares traded up above 1.7 percent following the tweet. (Get the latest quote here.)
Apple declined to comment on the news.
Icahn also took to Twitter to say that it was just over a year since his firm announced its large position in Apple, and that the stock is up 50.6 percent since then.
Icahn has previously pushed for Apple to engage in stock more buybacks, and trumpeted its pipeline of new products.
Apple analyst Brian Blair, managing director of Rosenblatt Securities, told CNBC on Thursday that he believes Icahn is going to suggest a breakup.
“I think it’s going to suggest that Apple break off this iTunes side of the business, along with Beats, and create a media platform,” he said.
Blair added: “I think he’s [Icahn] going to say, ‘Take Jimmy Iovine, take Dr. Dre, separate this iTunes unit and use you’re cash to really build out a media empire. Start maybe acquiring content, using the iRadio and this Beats streaming platform to create a separate but relevant business that can really help Apple grow, maybe even into the TV business.”
Read More Apple: We’re not shutting down Beats
The main reason Apple bought Beats is because iTunes is on the decline because of Spotify and other music streaming services, he said.
The Icahn letter also could have something to do with Apple Pay, Blair said.
“He [Icahn] was obviously spot on with eBay spinning off the PayPal side of the business, so he has some great views about unlocking shareholder value,” he said.
Icahn could have something to say about Apple becoming a credit card-type company in the long-term, he said.