The US comedian has banned all mobile phones and smart watches from his UK Total Blackout tour this month.
The move is aimed at stopping people filming his performances and posting them online – with anybody caught using them in venues being ejected from the premises.
Rock said the use of mobiles for texting, tweeting and recording performances is a “major intrusion” on the quality of his performance as a comedian.
He has urged fans to “take one night off from being the paparazzo of your own life” and just enjoy the concert without feeling the need to film it.
Rock said he was fed up with fans putting up clips of his performances on social media instead of enjoying the show.
He said: “There is also the added problem for comedians who spend months polishing their performances to a high state of hilarity only to have their punchlines shared in advance by illegal recordings of their show.”
The phones are placed for free in Yondr pouches which are locked as fans enter the arena.
Fans keep the fabric pouches with them at all times before they are then unlocked as they leave the venue.
Anybody wanting to use their phones during the show can go to a special area where the pouches are opened by staff.
Some fans are supportive of the move.
Scottish singer-songwriter Amy Macdonald, 30, who saw the comedian in Glasgow, tweeted: “How refreshing to not see 10,000 phones and people actually talking to each other. It’s the future!”
Twitter user TjPeddlico, who has also attended one of his shows, wrote: “It was beautiful to actually see so many people not using their phones like zombies!”
There has been strict enforcement of the ban.
At the gig in Glasgow, Chris Penman claimed he was kicked out by security guards for looking at his phone despite being given permission by a steward because he was waiting for an update on his father’s medical condition.
He told the Evening Times: “My dad is in the heart transplant ward in the Golden Jubilee in a really bad way.
“I explained the full thing but they still said I had to leave. I couldn’t believe it – I’m still baffled today. It’s just extraordinarily petty and unreasonable.
“I’m happy that my dad is doing better but I’m angry because my wife paid £140 for the tickets as a gift and we didn’t even get to see Chris Rock.”
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Other stars who have used Yondr pouches at their shows include fellow comedian Dave Chapell and musicians such as Alicia Keys, The Lumineers, and Guns N’ Roses.
Jack White is also planning to do the same for his upcoming tour, which includes dates in London.