The Kiku No. 8 satellite separated successfully from the rocket about 30 minutes into the flight, Japan Aerospace Exploration Agency spokesman Kiyotaka Yashido said.
The satellite was scheduled to deploy its solar panels later in the day and then begin a series of maneuvers over the coming week that, if all goes according to plan, should put it into its planned orbit next Tuesday morning, he said.
It will be used for telecommunications and to conduct sensitive measurements of time, calibrating a high-precision clock onboard with similar clocks on the ground, according to the agency.
The launch was originally scheduled for Saturday. The agency decided to delay it because of poor weather conditions that raised concerns of a possible lightning strike in the flight's early stages, the AP reports.
The H2-A rocket is the 11th launched by Japan and the first since Tokyo launched its third intelligence-gathering satellite in September.
The H2-A is the workhorse of Japan's space program.
After the incident with the shootdown of the Ilyushin Il-20 reconnaissance aircraft over the Mediterranean Sea, Russia will supply an S-300 anti-aircraft missile system to Syria