Elon Musk, the world's richest person, has tweeted he will pay $11bn (£8.3bn) in tax for this year.
Mr Musk, founder of electric car maker Tesla and aerospace manufacturer SpaceX, became the world's richest person earlier this year, BBC reported.
Last week, Mr Musk was named Time Magazine's Person of the Year.
That prompted Senator Warren to tweet: "Let's change the rigged tax code so 'The Person of the Year' will actually pay taxes and stop freeloading off everyone else."
US President Joe Biden is keen to increase taxes on the ultra-rich, although legislative plans have so far stalled in Congress.
Some senators, including Ms Warren, have backed the idea of taxing not only the income of America's richest citizens, but also the rising value of the assets they hold, like shares
Many of America's wealthiest citizens don't take a directly taxable salary. Instead, they hold their wealth in shares and other investments, then take out loans using those assets as collateral.