The equipment was stolen about a month ago from a van belonging to an independent production company, called Objective Productions, working for CBBC. It contained names, addresses and mobile phone numbers of children.
The BBC said it is taking the incident "very seriously" and said the data has not so far been misused.
It said in a statement, "This data was not lost by the BBC itself, but stolen from an independent production company working for CBBC. However we took the issue very seriously.
"There is absolutely no evidence this data has been misused and the measures we took were entirely precautionary.
"In the weeks since this happened, CBBC suspended new commissions and carried out a comprehensive review of objectives practices and we are now satisfied security of data is strong enough for production to resume."