If ESPN is having trouble, is the rest of television burnt toast?

Late on Tuesday, Disney reduced growth expectations for its vast cable network division, which contributes roughly half of its annual operating income and is anchored by what is considered the strongest channel around: ESPN.

Never mind that Disney’s chief executive, Robert A. Iger, aggressively defended ESPN’s overall health. By the end of trading on Wednesday, Disney shares had tumbled 9 percent, alarming investors across the entire entertainment industry.

Along with Disney’s decline were sharp drops in the stocks of other large media companies. Shares in Comcast, Time Warner, 21st Century Fox, CBS, Viacom, Discovery Communications and AMC Networks all were down on Wednesday. Discovery plunged 12 percent.

Some analysts cautioned that investors had mistakenly entered panic mode and that the companies largely delivered solid business results. Others said that the industrywide sell-off illuminated long-term fears about the fate of traditional media companies in a new digital world, where viewers are canceling their cable and satellite subscriptions as they spend more time watching on-demand streaming television that doesn’t include advertising.