T-Mobile US Inc. said Tuesday it wouldn’t charge customers for the data used to stream video from services such as Netflix, Hulu and HBO, opening a new front in the wireless price war.

The carrier will stream the videos at a lower quality, which will reduce the load on T-Mobile’s wireless network. The company also introduced new plans that raise the monthly service cost but include more data. T-Mobile is betting customers will opt to watch lower-definition video free on their smartphones instead of paying for higher resolution...