Ms Ferrier has admitted travelling to Parliament and speaking in the Commons after developing coronavirus symptoms, and then taking a train back to Scotland after testing positive.
Mr Blackford said she had made a “tremendous error of judgment” and now must “do the right thing for her constituents”.
He said Ms Ferrier’s SNP whip was withdrawn on Thursday morning when the party learned of her breaches of coronavirus rules.
Mr Blackford told BBC Radio Scotland’s Good Morning Scotland programme: “She has to reflect on the circumstances that she is now in.”
Asked if he is calling for her to resign, Mr Blackford said: “I would say to her that her position isn’t tenable, given the circumstances that we’re in, and she has to accept her own responsibilities of what she must do. I can’t force that upon her, she is no longer an SNP MP.
“I’m pretty angry at what has happened, it is not acceptable.
“It’s important that it is beyond reproach that everybody, absolutely everybody, must obey the rules and we have to think about the signal that gives the public and the sacrifices that people are having to make, and it’s in the light of that that Margaret will have to do the right thing.”
Statement: pic.twitter.com/rdWYhIauYv
— Margaret Ferrier MP (@MargaretFerrier) October 1, 2020
Mr Blackford insisted the SNP was unaware Ms Ferrier had taken a Covid-19 test on Saturday before travelling to Westminster to take part in a debate on coronavirus in the House of Commons on Monday.
By Ms Ferrier’s own account, she tested positive that evening, but she did not make clear whether she received the result before or after she spoke in the House.
The Rutherglen and Hamilton West MP said she took a test on Saturday afternoon after experiencing “mild symptoms”, meaning she should have self-isolated.
In a statement, she said she travelled home to Glasgow on Tuesday, where she has been self-isolating ever since.
She apologised for her actions and said there was “no excuse”.
Police Scotland said the MP informed them of her behaviour on Thursday and officers are “looking into the circumstances” along with the Metropolitan Police.
She could face a £4,000 (€4,414) fine for a first-time offence of coming into contact with others when she should have been self-isolating, under a law that came into force on the day of her positive test.
I have spoken with @MargaretFerrier this evening who fully accepts that what she did was wrong. Margaret will be referring herself to the parliamentary standards commissioner as well as the police. I am tonight suspending the whip from Margaret. https://t.co/1bCst4r5Pu
— Ian Blackford 🇺🇦🏴 (@Ianblackford_MP) October 1, 2020
Speaking to BBC Radio 4’s Today programme, Ms Blackford she had broken the law as well as coronavirus rules.
He added: “She has let herself down, and she has let her constituents, and indeed the country, down as well.
“I am asking her to reflect on her position – but I think it’s very clear what I’m doing.”
Communities Secretary Robert Jenrick told the same programme: “Margaret Ferrier has accepted that she has broken the law.
“That’s now a matter for the police, the authorities who are investigating the matter, and it is really for her to consider what her political future is, and for her party, the SNP.”
Scottish Conservative leader Douglas Ross branded Ms Ferrier’s decision to travel between London and Glasgow on a train with coronavirus symptoms as “reckless and dangerous”.
Mr Ross himself resigned as a Government minister over his party’s refusal to condemn Number 10 aide Dominic Cummings’s trip to Durham with his family at the height of lockdown while suffering coronavirus symptoms.
He said Ms Ferrier’s position is now “completely untenable”.
“No-one can take what she says with any credibility because she has flouted the rules at every opportunity when she first became aware of the symptoms back on Saturday,” Mr Ross said.
Responding to Ms Ferrier’s statement, First Minister Nicola Sturgeon tweeted: “This is utterly indefensible.
“It’s hard to express just how angry I feel on behalf of people across the country making hard sacrifices every day to help beat Covid. The rules apply to everyone and they’re in place to keep people safe.”
A number of SNP MPs, including David Linden whose Glasgow East constituency neighbours Ms Ferrier’s, have called for her to quit.
Meanwhile, shadow Scottish secretary Ian Murray demanded answers from Ms Sturgeon and Mr Blackford.
The Labour MP tweeted: “SNP in chaos & appear to be covering up serious breach of public health laws.
“FM & Blackford must hold press conference… to answer questions about what they did & didn’t know.”
SNP in chaos & appear to be covering up serious breach of public health laws. FM & Blackford must hold press conference tomorrow am to answer questions about what they did & didn’t know. Speaker contradicts SNP story. There can’t be 1 rule for the SNP, another for the rest of us.
— Ian Murray MP (@IanMurrayMP) October 1, 2020
An SNP spokeswoman insisted the party did not know until Thursday that Ms Ferrier had taken a test prior to travelling to London.
“Ms Ferrier informed the SNP on Wednesday, when she was in Glasgow, that she had tested positive,” she said.
“The SNP’s chief whip immediately informed Parliament authorities. The SNP only became aware on Thursday that Ms Ferrier had been tested prior to travelling to London and had travelled back to Glasgow, knowing that she had a positive result.”
On Monday, Ms Ferrier gave a four-minute speech in the Commons from 7.15pm and focused on the “economic health” of her constituents, calling for greater financial support.
