Stitchers often ended up with chronic back injuries from the unnatural sitting position, the newspaper reported.
The children are employed unofficially, through subcontractors, who pay them for each ball stitched.
A Canterbury rugby ball, which takes up to an hour to stitch, earns 11 rupees, about 25c.
Canterbury's sourcing manager, Jason Law, said the company was concerned about the claims.
"Child labour is unacceptable to us and is prohibited under our Supplier Code of Conduct," he told the Weekend Herald.
The company's initial investigations did not identify how Canterbury balls found their way into a homeworking environment.
Its manufacturing agreements with ball suppliers in Jalandhar are for Canterbury balls to be manufactured only in the factory or in supervised stitching centres.
"We do not permit unauthorised subcontracting. We do not permit homeworking," Mr Law said.
"Canterbury is doing everything it should and can be doing to get to the bottom of these claims."
Last week the company had a meeting with its supply base in Jalandhar and was "thoroughly assessing" its management and control processes of ball production.
Since the revelations, Canterbury has also met local labour rights Non-Governmental Organisation, the Sports Goods Foundation of India (SGFI), which is responsible for monitoring all members' ball stitching that takes place outside the factory.
Mr Law said Canterbury was investigating further, which would take time and involve multiple stakeholders, including an independent third party investigation agency and SGFI.
"When we have the findings of that investigation, we will take action as appropriate.
"We would withdraw business from a supplier if factory management were to refuse to collaborate on performance improvement.
"However, it should be noted that severing ties with a supplier can have huge implications for other workers in the community. It is simply too early for us to speculate on appropriate action."
Once Canterbury has completed its investigation, it will compile a report and a summary of findings will available to the public.
Canterbury of New Zealand was founded in 1904 and is named after the region where the company first started making knitwear.