"How is it possible to engage in meaningful discussions about long-term stockholder value while ... the CEO seems to be completely asleep or, even worse, either naive or willfully blind to these grave lapses of accountability and stockholder value destruction?" Icahn said in a letter to shareholders.
In a statement, eBay dismissed Icahn's letter as "cherry-picked old news clips," adding that both Andreessen and Cook "bring extraordinary insight, expertise and leadership" to the board.
"As we are sure our other shareholders would agree, we prefer to engage in more constructive and substantive discussions of why, in our view, PayPal and eBay are better together," eBay said. "Instead, Mr. Icahn unfortunately has resorted to mudslinging attacks against two impeccably qualified directors."
Andreessen is one of Silicon Valley's most prominent venture capitalists, while Scott is founder, former CEO and current board member of Intuit, the maker of TurboTax and other business and personal financial software.
"During Mr. Andreessen's time on the eBay board he has purchased large stakes in two former eBay subsidiaries, reaping significant personal riches," Icahn said in the open letter.
Icahn said Andreessen, who also sits on the board of Facebook, had invested in and actively advised five direct competitors of eBay - Boku, Coinbase, Dwolla, Jumio and Fab. Four of these, he said, were direct competitors to PayPal.
Icahn, citing a New York Times report, also said that in September 2009, an investor group that included Andreessen had preempted a planned IPO of Skype and bought 70 percent of the internet voice and video service for less than eBay had paid.
The group sold Skype to Microsoft for $8.5 billion about 18 months later, netting about $4 billion, Icahn said in his questioning of Andreessen's loyalty to eBay.
Others have also been critical of the deal, Icahn said, "but, until now, none have taken on the task of standing up to Mr Donahoe and this board."
Donahoe has been CEO of eBay since April 2012. EBay's shares, which closed at $54.59 on the Nasdaq on Friday, have risen about 45 percent over the period, outperforming the 35 percent rise in the Nasdaq composite index.
Icahn also took issue with Andreessen's investment in online shopping platform Kynetic, which eBay had sold back to its founders at a "low sale price" in 2011. Andreessen later invested $150 million in the company, for a paper gain of more than 100 percent a year later, Icahn said.
Icahn also raised concerns about having input from Cook when Intuit's Go-Payment service and PayPal were "direct competitors" in online payments processing.
"How can the board have a conversation about the strategy or performance of PayPal when a representative of a direct competitor who has so much at stake is in the room?"
EBay bought PayPal for $1.5 billion in 2002 and has considered hiving off the multibillion-dollar division.
But the company said last month that it had determined that PayPal would lose synergies with eBay's overall e-commerce business if it was independent.
"Let me remind you that we have an exceptionally strong board, with a diverse group of highly qualified directors. In fact we have a world class board," Donahoe said on a call with investors last month, explaining why eBay had rejected Icahn's proposal for a split.