Manning has tweeted a letter from the federal government that appears to show that she has been deemed inadmissible for entry.
The letter suggests Manning is not allowed in based on her conviction in the US on charges of espionage.
She was freed from prison in May after serving seven years of her sentence.
Former US president Barack Obama commuted her 35-year sentence before he left office earlier this year but did not pardon her.
Under Canada's Immigration and Refugee Protection Act, a foreign national can be inadmissible on a number of grounds related to "criminality" and "serious criminality".
The government letter cites the fact of her having been convicted of an offence in the US that would result in a prison term that carries a maximum sentence of at least 10 years in Canada.
It notes that the American charges under the espionage act would, if committed in Canada, "equate an indictable offence, namely treason" under the criminal code.
Manning apparently tried to cross into Canada at a New York-Quebec border crossing on Friday.
She said on Twitter that she would be challenging the denial of entry at an admissibility hearing.
Canadian Prime Minister Justin Trudeau was asked about the incident on Monday and said he had no comment.
The transgender soldier, born Bradley Manning, leaked diplomatic cables and other documents to Wikileaks in 2010, one of the largest breaches of classified material in US history.