Treasury Board president Jane Philpott, who was considered a star minister, said in a resignation letter that it was "untenable" for her to continue in the Cabinet because she could not defend the government.
Philpott, who was in overall charge of government spending, deprives Trudeau of another powerful female Cabinet minister just months ahead of an election that polls show he could lose.
Philpott's friend, former Attorney General and Justice Minister Jody Wilson-Raybould, testified last week that Trudeau and senior members of his government inappropriately tried to pressure her to avoid prosecution of a major Canadian engineering company in a case involving allegations of corruption in Libya.
Let our news meet your inbox. The news and stories that matters, delivered weekday mornings.
Wilson-Raybould resigned from Cabinet last month after being demoted to veteran affairs minister weeks earlier.
The scandal has rocked Trudeau's government. Gerald Butts, his closet adviser and best friend, also resigned last month and is scheduled to testify Wednesday before a Parliament justice committee in Trudeau's defense.
Trudeau has acknowledged raising the issue with Wilson-Raybould, but has said that was appropriate.
"I have been considering the events that have shaken the federal government in recent weeks and after serious reflection, I have concluded that I must resign as a member of Cabinet," Philpott wrote. "Sadly, I have lost confidence in how the government has dealt with this matter and in how it has responded to the issues raised."
Philpott, a physician, is a former minister of health and minister of indigenous services and was widely viewed as of one of Trudeau's most competent Cabinet ministers.
"I must abide by my core values, my ethical responsibilities and constitutional obligations," she wrote. "There can be a cost to acting on one's principles, but there is a bigger cost to abandoning them."
Trudeau told a Liberal Party rally in Toronto that he was disappointed but understood why Philpott had left.
"Concerns of this nature must be taken seriously and I can ensure you that I am," said Trudeau, who did not specifically address Philpott's stated reasons for leaving. He also thanked her for serving in his Cabinet — something he notably did not do when Wilson-Raybould quit.
The leader of the opposition Conservative Party, Andrew Scheer, said at a news conference that Philpott's resignation demonstrates "a government in total chaos" and called again for Trudeau to resign and for a police investigation of the affair.
Wilson-Raybould testified last week she was pressured to instruct the director of public prosecutions to negotiate a remediation agreement with SNC-Lavalin. The agreement would have allowed the company to pay reparations but avoid a criminal trial on charges of corruption and bribery. But Wilson-Raybould said the pressure was not illegal and said she was not instructed to interfere.
If convicted criminally, the Montreal-based company would be banned from receiving any federal government business for a decade. SNC-Lavalin is an economic force in Canada, with 9,000 employees in the country and about 50,000 worldwide.