The song became a worldwide hit, topping charts in O'Connor's native Ireland, Australia, Austria, Canada, Germany, Netherlands, New Zealand, Norway, Sweden, Switzerland, and the United Kingdom. It also became a top-five single in France and a top-20 in Denmark. The single was certified platinum in Austria and the United Kingdom, and gold in Germany and Sweden.
In the United States it spent four weeks at the top of the Billboard Hot 100; in addition, it was a number-one in Billboard Alternative Songs chart and reached number two on Billboard Adult Contemporary chart. It became the third best-selling single of 1990, the 82nd best-selling single of the 1990s, and was certified platinum by the Recording Industry Association of America in April 1990. The song's popularity sent I Do Not Want What I Haven't Got to the top of the Billboard 200 where it stayed for six consecutive weeks.