The firm's Falcon rocket, topped by an unmanned Dragon freight capsule, lifted clear of its Florida pad at 03:44 EDT (07:44 GMT; 08:44 BST).
The initial climb to an altitude some 340km above the Earth lasted a little under 10 minutes.
Within moments of being ejected, Dragon opened its solar panels.
It will take a couple of days to reach the station. The plan currently is for the vessel to demonstrate its guidance, control and communications systems on Thursday, at a distance of 2.5km from the International Space Station (ISS).
If those practice proximity manoeuvres go well, Dragon will be allowed to drive to within 10m of the station on Friday. Astronauts inside the platform will then grab the ship with a robotic arm and berth it to the 400km-high structure.
They will empty Dragon of its 500kg of food, water and equipment, before releasing it for a return to Earth at the end of the month.
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