The newspaper cited people familiar with US officials' early assessment of evidence uncovered in the investigation into the crash, which killed 260 people.
The first officer, who was flying the Boeing 787 Dreamliner, asked the more experienced captain why he moved the switches to the "cutoff" position after it climbed off the runway, the report said.
The first officer expressed surprise and then panicked, while the captain seemed to remain calm, the WSJ reported.
A preliminary report released last week by India's Aircraft Accident Investigation Bureau depicted confusion in the cockpit shortly before the June 12 crash, and raised fresh questions over the position of the critical engine fuel cutoff switches.