BRUSSELS—Iran will ship about 11 metric tons of heavy water out of the country in the next couple of days, according to people familiar with the plans, defusing a conflict with the U.S. and others over the Iranian nuclear deal.

Earlier this week, the head of the International Atomic Energy Agency, Yukiya Amano, expressed concerns that Iran had for the second time exceeded a 130-metric-ton threshold for its heavy-water stockpile. A metric ton is equivalent to 1.1 short tons.

He...