In May, Kara Burke and Tom Cairns thought they had found their ideal house: a nicely-updated older three-bedroom home in Worthington, Mass.

But they didn’t make an offer because it didn’t have high speed Internet.

“We wouldn’t choose a house that didn’t have electricity,” Ms. Burke, 26 years old, said as she explained why. “It’s right on par with those things.”

As the Internet becomes central to the way Americans work and live, the digital divide is taking on greater economic significance. Students without Internet access at home may struggle to keep up with school assignments. Towns with less access find themselves falling behind economically, researchers say. Now, the availability of speedy Internet service is starting to affect Americans’ biggest purchase: their homes.

Real-estate agents across the country say more buyers like Ms. Burke and Mr. Cairns are turning their noses up at homes without fast Web access. Some studies suggest those buyers are having a keen effect on home prices. A nationwide study released on Monday by researchers at the University of Colorado and Carnegie Mellon University finds fiber-optic connections, the fastest type of high speed Internet available, can add $5,437 to the price of a $175,000 home—about as much as a fireplace, or half the value of a bathroom.