The billionaire entrepreneur said on his social media platform X on Monday that the giveaway would be his first initiative of its kind "of many", but provided no details on how the plan would be implemented.
According to the latest US census data, there are just over 70 million people under the age of 18 in the nation.
At SpaceX's current share price, distributing one share to each child would cost more than $US10 billion.
Musk's fortune is currently estimated at more than $US900 billion ($A1.3 trillion) by Forbes magazine, consisting largely of shares in SpaceX and electric carmaker Tesla, which he also heads.
His announcement may have been prompted by a move over the weekend by rival artificial intelligence company Anthropic, which said it would initially place 5 per cent of its shares into a fund intended to benefit the public.
In response, Musk wrote to Anthropic on X: "I recommend giving the shares directly to the public."
SpaceX is the parent company of Musk's artificial intelligence company xAI.
SpaceX shares initially surged following the company's stock market debut in June, but have since fallen well below their highs of more than $US200.
The stock is now trading below $US150 ($A215), while questions remain about the company's valuation of around $US1.9 trillion.
SpaceX's rocket business remains relatively small compared with its market valuation, which largely reflects investor expectations of future success in artificial intelligence promised by Musk.
However, SpaceX currently lags well behind AI leaders Anthropic and OpenAI, the developer of ChatGPT.
