Members of the audience shouted "fire, fire!" at the cast and crew on stage during the evening performance on November 24.
One member of the crew grabbed a fire extinguisher to deal with the 'minor' fire.
The audience were evacuated for around 20 minutes.
Paedophile arrested at Leeds Bradford Airport after travelling from Ireland to meet ‘13-year-old girl’
Met Office issues thunderstorms and torrential rain weather warning for Leeds as heatwave comes to abrupt end
Developers admit planning breaches in construction of Leeds retirement flats
Aasia Majeed: Police launch urgent appeal to trace Leeds mum missing with one-year-old child
Andre Rieu, Europe's Strongest Man and Magic Mike Leeds Arena shows could be at risk if city wins Eurovision bid
However, the show - which is earning rave reviews - resumed once the stage had been made safe.
Audience member Lizzie Murphy said: "There was even more adventure than expected at the opening night of #wendyandpeterpan @LeedsPlayhouse tonight when the scenery caught fire and the audience had to evacuate."
In a further tweet, she added: "Members of the audience were shouting “fire, fire!” to alert the cast and crew who grabbed the nearest fire extinguishers. Thankfully it was only minor, the audience was allowed back in after about 20 minutes and the show resumed once the stage had been made safe."
Speaking to the Yorkshire Post, Lizzie added: "It was during a dramatic fight scene filled with lots of pyrotechnics when one or two sparks must have reached a chair on the left hand side of the stage as well as some bunting that was hung up.
"The audience started shouting 'fire".
"Once the cast and crew realised what was happening they grabbed the nearest fire extinguishers and tried to put the fire out but there was still some persistent smouldering bunting.
"They evacuated us out of the building for a while and then we were allowed back in for the last 20 minutes of the performance. Luckily it was only a minor incident but they dealt with it brilliantly."
Fellow audience member Lynda Smithers added: "They resumed the performance really quickly once the safety checks had been done and carried on with the show very professionally. I thought they were really good."
A Leeds Playhouse spokesperson said: “We can confirm that a small fire caused by a pyrotechnic effect briefly occurred on stage last night during our first public performance of our large-scale festive production Wendy & Peter Pan.
"We are pleased to report it was quickly extinguished by a member of our stage crew, who are there to deal with these kind of eventualities, no-one was injured and our evacuation procedures were implemented smoothly.
"Following safety checks the audience re-entered the theatre to watch the end of the show. The incident has been reviewed and we are satisfied that the rest of the run will proceed safely.”