Rocket Lab's 17m-long (56ft) Electron lifted off from the Mahia Peninsula, in the North Island, the firm said.
The test flight was the first launch from New Zealand and is a major first step in an emerging market: launching cheap disposable rockets to carry small satellites and other payloads.
The company plans to start frequent commercial launches later this year.
Poor weather conditions had pushed the launch into the fourth day of a 10-day window and the Electron finally cleared its pad at 16:20 local time (04:20 GMT).
