Kenzo and ObbyRaidz, whose channels predominantly feature them playing Minecraft, reported receiving messages demanding money in exchange for dropping two claims against them.
These messages threatened that refusal to pay would result in a third copyright "strike", which, according to Google, results in a YouTube channel being "subject to termination".
The extorter's YouTube account has been deleted after the illegal activity was made public.
Kenzo and ObbyRaidz both received messages demanding payment ranging from $75 to $400 (£58 to £309) be sent via Paypal or Bitcoin.
Neither paid and British YouTuber Kenzo, who has 60,000 subscribers, took to social media to plead for help after one of his videos was taken down by the extorter's second fraudulent copyright strike,
In its response to Kenzo's tweet, YouTube said both of the copyright claims against him had been "obviously abusive" and it had reinstated his video to its platform.
"This is an example of a fraudulent legal request, which we have zero tolerance for," it said in a statement. "We [have] terminated [the extorter's] channel."
Google, which owns YouTube, did not respond to a request for information regarding how YouTube intended to prevent such extortion attempts in the future.
How easy is it to make a copyright claim?
A successful " copyright takedown notification" results in a video being removed and the infringing YouTube channel receiving a copyright strike.
To make such a claim, an individual must provide their contact information and a description of the copyright they say has been infringed by the video in question.
The applicant must also accept possible legal consequences for "false or bad faith" allegations of copyright infringement.
But US-based YouTuber ObbyRaidz has now called the system "broken", in a video posted to his YouTube channel.
"Anybody can do it," he said. "They made it so easy to take somebody's channel down - they strike a few videos and your channel is terminated.
"The way I look at it, YouTube just put a Band-Aid on a much bigger issue," he said, referring to the deletion of the extorter's account.
"This is something that can affect more channels in the future and they need to fix this right now."
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Copyright strikes and Content ID
YouTube has come under fire for its Content ID system, which automatically determines whether a video contains copyrighted material.
This system was criticised in 2018 after it resulted in a YouTuber receiving a copyright infringement notice for including his own song in a video.
A copyright takedown notification, in contrast, results from an application submitted to YouTube by an individual.
These claims, however, do not necessarily lead to a takedown and a strike being placed on a channel.
For example, an individual can choose to make a copyright claim that, if successful, keeps a video online but directs any ad revenue towards the original copyright holder.
This type of copyright claim is becoming increasingly commonplace, with YouTuber MrBeast - who has more than 14.8 million subscribers - revealing that five of his most recent videos have all been demonetised under such claims.