The Globe and Mail reported that the arrest of Wanzhou Meng was at the request of American authorities.
Meng is the deputy chairperson of Huawei's board and the daughter of the company's founder, Ren Zhengfei.
News of the US Justice Department probe into whether Huawei has violated sanctions on Iran was reported by The Wall Street Journal in April.
A Canadian Justice Department spokesman Ian McLeod was quoted in the report as saying: "“Wanzhou Meng was arrested in Vancouver on 1 December. She is sought for extradition by the United States, and a bail hearing has been set for Friday.
“As there is a publication ban in effect, we cannot provide any further detail at this time. The ban was sought by Ms Meng."
The report quoted an unnamed source as saying the US was alleging that Meng tried to evade the US trade embargo against Iran.
Earlier this year, the US Department of Commerce slapped a seven-year ban on another big Chinese telco equipment maker, ZTE, claiming that the company had made false statements during talks in 2016 over a charge of shipping telco equipment to Iran and North Korea.
ZTE shut down its main business activities in the US on 9 May.
But following the intervention of US President Donald Trump, a deal was worked out for ZTE to return to business by paying a fine of US$1 billion, changing its management team and depositing US$400 million in an escrow account against possible future transgressions.
iTWire has contacted Huawei for comment.