A judge sitting in London ruled the injunction, which will also impact on other sports, was justified as the operators of the "very popular" website were making millions of pounds from copyright infringement.
The application for an injunction came from the Football Association Premier League Ltd (FAPL), which owns the copyright in broadcast recordings of all Premier League matches.
Allowing the FAPL application, the judge said FirstRow was "profiting from infringement on a large scale" by making match broadcasts available "to persons who are not entitled to view them either because they have not subscribed to the broadcaster's service, or because the broadcaster has only been licensed by FAPL for a different territory".
The injunction is against the UK's six main retail internet service providers (ISPs) - British Sky Broadcasting, BT, Everything Eveywhere, TalkTalk, Telefonica UK and Virgin Media.
Chancery Division judge Mr Justice Arnold said his orders require the ISPs to take measures "to block or at least impede" access by their customers to the FirstRow website.
The FirstRow ban has been obtained before the start of the next Premier League season, which kicks off on Saturday August 17.
The judge said the FAPL application was supported by eight other organisations including rightholders for golf, darts, snooker and rugby, as well as other football bodies. All had provided witness statements confirming that FirstRow was not licensed by them to exploit their copyright in matches.
FirstRow was a website operating for some time through a number of domain names, some of which had been seized by the US Department of Homeland Security, said the judge.The streams indexed on FirstRow were provided by third-party streamers using one of a number of user-generated websites (UGCs).
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