Walt Disney Co. is banning advertising from Netflix Inc. across its entertainment TV networks, according to people familiar with the situation, a sign that the marketing wars over streaming-video are escalating as media giants battle each other for subscribers.

Disney, Comcast Corp. and AT&T Inc. are set to spend hundreds of millions of dollars on advertising over the next year to attract consumers to their new streaming-video services as they look to compete with industry juggernaut Netflix. Netflix spent $1.8 billion on...