Mr Bezos built Amazon into a shopping and entertainment behemoth but has faced increasing activism within his own workforce and stepped up pressure from critics to improve working conditions.
Labour groups and Amazon workers have claimed that the company offers its hourly employees not enough break times, puts too much reliance on rigid productivity metrics and has unsafe working conditions. An effort to unionise workers at an Amazon warehouse in Alabama failed earlier this year.
Robert Reich, former secretary of labour under President Bill Clinton and a professor of public policy at University of California, Berkeley, wrote on Twitter that Mr Bezos has crushed unionising attempts for decades.
"Amazon workers don't need Bezos to thank them. They need him to stop union-busting - and pay them what they deserve," Mr Reich wrote.
Billionaire Jeff Bezos has successful first space flight
Mr Bezos stepped down as Amazon CEO in July, allowing him more time for side projects including his space exploration company Blue Origin. He has said he finances the rocket company by selling $A1.4 billion in Amazon stock each year.
After the spaceflight, Mr Bezos awarded $A136 million donations through a new philanthropic initiative to both DC chef Jose Andres and CNN contributor Van Jones to put towards any charity or nonprofit of their choice. Jones has founded a number of nonprofit organisations and Andres' nonprofit group World Central Kitchen provides meals to people following natural disasters.
Nevertheless, Earl Blumenauer, who is on the tax-writing Ways and Means Committee, proposed on Tuesday legislation that would tax space travel for non-scientific research purposes.
"Space exploration isn't a tax-free holiday for the wealthy," said Mr Blumenauer, an Oregon Democrat.
"Just as normal Americans pay taxes when they buy airline tickets, billionaires who fly into space to produce nothing of scientific value should do the same, and then some."
Others tied his spaceflight to reports that Mr Bezos hasn't paid his fair share of taxes. According to the nonprofit investigative journalism organisation ProPublica, Mr Bezos paid no income tax in 2007 and 2011.
"Jeff Bezos forgot to thank all the hardworking Americans who actually paid taxes to keep this country running while he and Amazon paid nothing," Democratic Senator Elizabeth Warren tweeted.
Allen Adamson, co-founder of marketing consultancy Metaforce, said it is challenging for Mr Bezos to say where the money from the space trip is coming from without being offensive. He says he should have left out those comments and focused on thanking the Blue Origin team.
"For people who have an issue with inequality and his compensation versus the average employee compensation, this was rocket fuel," Mr Adamson said.