Formula 1 Karting Ltd, of Forge Road, admitted three health and safety offences after the children were made ill by the fumes.
The firm has since improved ventilation and fitted kart catalytic converters.
A spokesman for the company said it was an "isolated incident" and the children had not needed hospital treatment.
The prosecution was made before town magistrates by Gateshead Council.
The hearing heard how the children were celebrating a birthday when one of the parents, a nurse, noticed they were ill and complained.
She checked the children out and they did not need to go to hospital.
'Cavalier approach'
Council officials investigated and discovered that exhaust fumes from the karts had reached "dangerous" levels within the building, the court was told.
The company had been relying on opening fire doors to ventilate the building and remove the exhaust gases and no routine monitoring was being carried out, the hearing heard.
A prohibition notice was served closing the business until improvements were made. The firm was fined £12,000 for each offence and ordered to pay £5,000 costs - a total of £41,000.
'Isolated incident
Paul Dowling, head of regulatory services for the council, said: "This company appeared to be taking an extremely cavalier approach to the health of their customers and staff.
"We were very surprised and appalled by the levels of carbon monoxide - it was so serious we felt we had had no alternative but to shut them down immediately.
"Hopefully, this substantial fine will send a clear message to other indoor karting operators that they must take their responsibilities, both to their customers and to their staff, much more seriously."
Adrian Styles, spokesman for Formula 1 Karting, said: "This was an isolated incident which happened well over a year ago and we have since been given a clean bill of health.
"We have installed a full ventilation system. The children were not taken to hospital and later attended a birthday party."
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