The SpaceX CEO said the offshore platform, named Deimos after one of the moons of Mars, is already under construction and will be ready for the Mars-bound craft at some point next year.
SpaceX ultimately plans to establish Starship launch sites around the world, and has already acquired disused oil rigs in order to convert them into spaceports.
Deimos and another rig named Phoibos are currently being converted in the Port of Brownsville near SpaceX’s Starbase facility in Boca Chica, Texas.
Each rig cost around $3.5 million (£2.6m), with Mr Musk tweeting in February: “I hope we don’t go bankrupt building them.”
SpaceX completed the first successful landing of a Starship craft following a high-altitude flight test earlier this month, with an orbital test planned for the next SN16 prototype before July.
Testing of the next-generation rocket is also taking place in Texas, where Mr Musk moved last year in order to focus his attention on Starship’s development.
SpaceX has already secured a $3 billion contract with Nasa, which will see the US space agency work with the private space firm to return humans to the Moon aboard a Starship rocket by 2024.
Mr Musk ultimately hopes to build hundreds of Starships in order to establish a permanent human colony on Mars. The first crewed trips to the Red Planet could happen as early as 2024, according to the technology billionaire.
June’s orbital Starship SN16 test will be the first to use SpaceX’s 70-metre tall Super Heavy rocket booster, which will help propel the 50-metre craft into orbit.
The booster stage will separate from Starship roughly 170 seconds into the 90-minute flight, which will take an uncrewed craft from the Boca Chica facility to Hawaii.
Combining Starship with the Super Heavy booster will make it the most powerful launch vehicle ever developed, taking the crown from the massive Saturn V rocket system used by Nasa in the 1960s and 1970s to take humans to the Moon.
Future versions of the main Starship craft will feature “private cabins, large common areas, centralised storage, solar storm shelters and a viewing gallery,” according to SpaceX, with each one capable of carrying up to 100 people. Mr Musk has previously revealed his ambition to travel to Mars aboard a Starship within his lifetime.