The forecast comes after years of excess supply, which last year prompted major oil producers to agree to cuts in output.
The IEA said the oil market was now "very close to balance."
But the organisation predicted supply would grow in coming months, with US oil-producing firms driving the increase.
The IEA said it expected non-Opec production, of which the US and Russia account for the biggest chunk, to rise by 485,000 barrels a day in 2017 to a total of 58.1 million barrels a day.
US production had already climbed to 9 million barrels a day in March, up from a September low of 8.6 million barrels per day.
The IEA said it expects demand to increase by just 1.3 million barrels a day in 2017, rising to a total of about 97.9 million barrels a day.
That is less than the organisation had anticipated previously and could prove an "optimistic" forecast, it said.
Demand for oil is expected to slow for the second year in a row, the International Energy Agency has said.