Liz Truss announced her Cabinet on Tuesday, with Kwasi Kwarteng, Suella Braverman and James Cleverly receiving the top jobs.
However, one unnamed MP is said to have complained that "white straight males" are not included.
It is the first time any of the four Great Offices of State have not been held by a white man.
An MP is reported to have claimed white men "never get a sniff at anything" after Liz Truss unveiled the most diverse Cabinet in UK history.
The new prime minister announced her picks for the top jobs in government, and for the first time in British history, no white man will hold any of the four great offices of state.
Truss - herself the third female prime minister - named Kwasi Kwarteng as her chancellor of the exchequer, Suella Braverman as her home secretary and James Cleverly as her foreign secretary.
Kwarteng's parents came from Ghana in the 1960s, and his appointment makes him the first Black finance minister.
Braverman, whose parents came to Britain from Kenya and Mauritius six decades ago, succeeds Priti Patel as home secretary.
Cleverly, whose mother is from Sierra Leone and whose father is white, has in the past spoken about being bullied as a mixed-race child and has said the party needs to do more to attract Black voters.
But while their appointments have been overwhelmingly positive, at least one Conservative MP is reported to be unhappy.
The unidentified MP told the Telegraph's chief political correspondent Camilla Turner: “There are a lot of talented men in the 2019 intake - white straight males that never get a sniff at anything.
“You’ve got these great MPs and they’ve just been totally overlooked. It’s time to reward people based on talent rather than what they look like.”
In February 2020, a report revealed a majority of MPs form non-white backgrounds have experienced racism at Westminster.
According to a survey by ITV News, with 62% of 37 respondents indicated they had faced racism or racial profiling whilst on the Parliamentary estate.
British governments have, until a few decades ago, been predominantly made up of white men.
Watch: Liz Truss's new-look Cabinet meet for first time to consider energy bills plan
In 2001, 91% of Conservative MPs were men - and all of them were white.
It took until 2002 for Britain to appoint its first Black cabinet minister when Paul Boateng was appointed chief secretary to the Treasury.
At the time, Boateng said: "First and foremost I am a cabinet minister. My colour is part of me but I do not choose to be defined by my colour.
"I work for a world in which people are not judged by their colour but by the content of their character. I want to be judged by my work in this position."
With the announcement of her top table, Truss has faced some criticism that she has seemingly purged her team of supporters of her defeated rival, Rishi Sunak
Dominic Raab, Grant Shapps, Steve Barclay, George Eustice and Shailesh Vara were among some of those who were banished to the back benches after supporting the former Chancellor during the leadership race.
The wife of one sacked minister branded Truss and "imbecile" after he was removed.
Felicity Cornelius-Mercer, wife of former veterans' affairs minister Johnny Mercer, said the Cabinet system “stinks” and “treats people appallingly” after her husband was removed.
Mrs Cornelius-Mercer tweeted a picture mocking Ms Truss as a character from The Muppets television show and giving an account of Mr Mercer’s exit discussions. She said: “He asked her ‘why would you do this, who is going to be better at this role than me, which of your mates gets the job, you promised a meritocracy?’
“PM – I can’t answer that Johnny.
“This system stinks & treats people appallingly.
“Best person I know sacked by an imbecile @trussliz.”
Mercer had tweeted a lengthy resignation statement accompanied by the words: “I will be spending time with my family and doing no media requests.”
Deputy PM and health secretary Therese Coffey insisted Truss appointed a diverse “Government of all the talents” including some people who did not support her.
“This is I think a Government of all the talents that we have in this party,” the new Health Secretary and Deputy Prime Minister told Sky News.
“Liz has appointed a Cabinet of a mixture of whether it’s people of her proactive supporters, people who did not support her as well”.