"Viacom is a company built from lawsuits, look at their history," Schmidt said on Friday.
"Look who they hired as CEO, Philippe Dauman, who was the general counsel for Viacom for 20 years," he added.
Dauman, a long-time advisor to Viacom Chairman Sumner Redstone, served as general counsel from 1993 to 1998 and served as deputy chairman from 1996 to 2000. Before joining Viacom, Dauman was a partner at law firm Shearman & Sterling.
Viacom Chairman Sumner Redstone responded by saying that despite a long history of suing rivals, he preferred to resolve disputes outside of court.
"I would rather be a lover than a fighter," Redstone told reporters at the Allen & Co. conference in Sun Valley, Idaho.
Viacom has demanded that YouTube takes down hundreds of thousands of segments from its popular programs including "The Daily Show with Jon Stewart," "The Colbert Report" and "South Park."
Viacom has said it sued Google because the companies failed to reach a distribution deal that adequately compensated Viacom for its content. A court hearing begins later this month.
Schmidt, who said he had spoken with Dauman while at the conference, also said Google intended to fight the suit.
He alluded to Viacom's $2.4 billion antitrust suit against TimeWarner in 1989. That suit claimed Time Warner's HBO pay cable movie service tried to put Viacom's Showtime out of business by intimidating cable operators and Hollywood studios to give preferential treatment to HBO.
The suit was ultimately settled out of court by 1992. As part of the settlement, Time Warner paid $75 million and agreed to purchase a cable system owned by Viacom for an above market price, as well as agree to distribute Showtime more broadly on Time Warner cable television system.
The two companies eventually agreed to merge their rival comedy cable networks to form Comedy Central, now home to popular shows hosted by Jon Stewart and Stephen Colbert.
"We have engaged in a lot of litigation. We sued John Malone. We sued Time Warner. We sued Barry Diller. I don't enjoy battles," Redstone said.
For its part, Google has been the target of numerous lawsuits, most recently one filed by the Australian government charging the company with promoting deceptive business practices with its lucrative pay-per-click advertising system.
Separately, Schmidt said the surge in popularity of Internet social networks such as News Corp.'s MySpace and Facebook would ultimately be positive for Google.
Google, whose main source of revenue comes from selling advertising based on text keyword searches, relies on its catalog of documents from the Web, its so called index.
But sites such as Facebook, whose members and third party companies have rapidly created new content for Facebook, prevent the indexing of its pages.
Schmidt said the closing off of social networks was a "transient" phase and that these companies will eventually see the value of open borders.
Google shares rose 1.2% to $551.75 on Nasdaq. Viacom's Class B shares were down 0.64% at $41.72.