Nusrat Ghani, 49, who lost her job as a junior transport minister in February 2020, told the Sunday Times she had been told by a whip - an enforcer of parliamentary discipline - that her "Muslimness" had been raised as an issue in her sacking.
"The prime minister has asked the Cabinet Office to conduct an inquiry into the allegations made by Nusrat Ghani MP," Downing Street said on Monday.
"As he said at the time, the prime minister takes these claims very seriously."
The government's chief whip, Mark Spencer, said he was the person at the centre of Ghani's allegations. He said they were completely false and defamatory.
"I have never used those words attributed to me," he said.
Johnson met Ghani to discuss the "extremely serious" claims in July 2020, a spokesperson from the prime minister's office said on Sunday.
Downing Street said that when the allegations were first made, Johnson recommended she make a formal complaint to the Conservative Campaign Headquarters.
"She did not take up this offer," Downing Street said.
Ghani's allegation came after one of her Conservative colleagues said he would meet police to discuss accusations that government whips had attempted to "blackmail" MPs suspected of trying to force Johnson from office over lockdown parties.
