WASHINGTON—Online streaming startup Aereo Inc. violated the copyrights of major television broadcast networks by retransmitting programs to users’ Internet devices for a fee, the U.S. Supreme Court ruled this morning.

In what some observers have called the most important copyright challenge to reach the high court in a decade, ABC and other networks argued that Aereo was violating their exclusive right under the Copyright Act to “publicly perform” their works. A divided panel of the U.S. Court of Appeals for the Second Circuit disagreed.