The End Of Longing is the former Friends actor's playwriting debut, which is showing in London until May.
Perry received a standing ovation after its premiere on Thursday evening, but critics have not been so supportive.
The Guardian gave it two stars, calling it "flimsy" with characters that "never really develop".
"It feels more like an extended sitcom in which there is little going on behind the lines," the paper said. "What works in half-hour bites on television looks decidedly thin on the stage."
Matthew Perry plays the lead character in the play - an alcoholic photographer who falls in love with a prostitute.
"There's so little believable connection or tenderness between these friends and lovers, and their characters have about as much depth as a puddle in a heat wave," wrote Holly Williams in her two-star review in The Independent.
According to Dominic Cavendish in The Telegraph, the play is "a curious waste of time, money and effort".
Quentin Letts in the Daily Mail was kinder, saying: "[Director] Lindsay Posner's production is coolly staged, well acted and thoroughly watchable."
"I enjoyed it, though fully expect to forget much of it within a week or so."
Theatre website WhatsOnStage gives the show four stars, commenting that Perry's writing shows "great promise".
But there's some good news for Perry. The Times gives it four stars, with Ann Treneman saying it is "funny" and "often laugh out loud", noting that Perry "looks like a man with something to prove to himself and us - and he has certainly done that".
Many reviewers were agreed the play would be most enjoyed by Friends devotees.
Indeed, several fans and celebrities took to Twitter after the show to express their enjoyment of it.
Actress Sadie Frost tweeted: "I really enjoyed such a wonderfully written play. All the performances were very strong - Perry was incredible."
Busted member Charlie Simpson also said he had "really enjoyed watching Matthew Perry", while EastEnders actress Bonnie Langford congratulated the cast on a "fabulous opening night".
Last week, Perry spoke to arts correspondent Rebecca Jones about his interest in writing, dating back to when he was the only Friends actor in the show's writers' room.
A play written by and starring Matthew Perry has received a mixed response from critics on its opening night.