The first shows of a two-week long run started yesterday in Queen's Park, Glasgow, in an inflatable showdome.
But the capacity of the standard seating in the venue was slashed by more than half at the last minute, meaning parents and children were reportedly turned away at the doors.
Organisers of the live show said the problem had been caused after the council informed them yesterday morning the seating stand would have to be reduced from 440 to 216 seats for each show due to a "technical discrepancy" which they did not have time to rectify.
But Glasgow City Council said the action had been taken due to potential safety concerns.
Other ticket-holders for the shows, which will run until September 13, have received an email advising their bookings have been cancelled. They have been offered a full refund and free replacement tickets.
Last night, no-one from Minor Entertainment, which produces the show, could be contacted. But with 15 of the 36 shows showing as sold out on the website booking system, it is thought thousands could be affected.
In the Night Garden, featuring the adventures of characters Iggle Piggle, Makka Pakka, Upsy Daisy and Tombliboo Ooo, is a BBC series which ran from 2007 until 2010.
Several angry customers left comments on social media sites yesterday. One Twitter user wrote: "Well done, disappointing hundreds of toddlers due your last minute restriction on In The Night Garden!! #GCC #MakingChildrenCry."
On the In the Night Garden Live Facebook page, comments included: "I watched a wee boy with special needs being turned away this morning on the day of his birthday how bad is that! Disgusting Glasgow council."
A statement on the Facebook site for In the Night Garden Live said: "At 8.45am on Saturday 30th August Glasgow City Council told us that they are imposing a restricted capacity on our seating stand. Instead of having 440 standard seats available we now have only 216. We have staged the show in 25 venues in the last five years.
"Glasgow City Council itself approved 440 standard seats when we last visited in 2010. The council's reasons for the restriction relate to a technical discrepancy in the engineering calculations which we do not have time to remedy."
But last night a spokeswoman for Glasgow City Council said: "Having inspected the In the Night Garden's showdome and seating structure, a structural engineer from the council's building control service had concerns with its construction and also in terms of it specifically not being built in accordance with original design intent.
"This led to possible safety concerns. The issues were discussed with the show's engineer who agreed with our concerns during a telephone conversation yesterday."
She added: "Not wanting to disappoint audiences, over the last few days we have worked closely with the on-site contractor to make enhancements to the seating structure to allow shows to run, albeit at a reduced capacity.
"The intention is that further dialogue will take place in the coming week with the representatives of the show's licence-holder to assess whether further work can be done to allow a full capacity audience."
In an email sent to customers who had their bookings cancelled, Andrew Collier, creative director of Minor Entertainment, said he was "truly sorry".