Sushma Swaraj warned that the global online retailer, which has made a significant push into India in recent years, would have to issue an "unconditional apology" for selling the items, which were pointed out to her on Twitter.
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Ms Swaraj was contacted about the doormats on Tuesday afternoon by "Atul Bhobe", a Twitter user with 60 followers, who sent a screenshot of several Indian flag doormats and urged her: "Amazon Canada must be censured".
The doormats, just some of a range of similar products bearing the flags of various countries, were selling for C$35.99.
Within hours the external affairs minister, who is known for her active Twitter account, responded: "Indian High Commission in Canada: This is unacceptable. Please take this up with Amazon at the highest level."
An hour later she warned, also on Twitter: "Amazon must tender unconditional apology. They must withdraw all products insulting our national flag immediately.
"If this is not done forthwith, we will not grant Indian Visa to any Amazon official. We will also rescind the Visa issued earlier."
Amazon responded with a one-line statement, saying: "The item is no longer for sale on the site."
Ms Swaraj is known for frequently responding to Twitter users' questions and pleas for help, including one Indian user who asked her to help free his sister who was allegedly being held illegally in a Dubai hotel room.
The spat is awkward for Amazon, which is expanding aggressively in India in an attempt to take advantage of the country's growing middle class and strong economic growth.
In 2014, its founder Jeff Bezos donned a white Indian wedding suit and climbed aboard a truck in Bangalore, India's technology capital, and handed a giant cheque for $2 billion, the amount it planned to invest in the country, to its new Indian operations chief.
Since then the company has spent billions more in India and taken on heavy losses — about $500 million last year — as it fights for market share alongside its domestic rivals Flipkart and Snapdeal.
But Ms Swaraj's threat also gives a glimpse of the tensions within the ruling Bharatiya Janata party between its nationalist roots and its more pro-business elements.
While the foreign minister was tweeting her threat, Narendra Modi, the country's prime minister, was wooing foreign investors at an international business summit in his home state of Gujarat.
Mr Modi told the audience at the Vibrant Gujarat conference on Monday: "You will all see that soon India will be the easiest and one of the best places to do business."
Separately on Wednesday, Amazon agreed to pay a $1.1 million fine and change its practices to settle a dispute with Canadian regulators.
Regulators found that the "list price" for items sold on Amazon.com.ca, which refers to what is purportedly the original price of an item, did not in fact reflect the market prices of the items in question. Amazon agreed to change its practices as a result.