Almost nine in 10 (86%) children aged between eight and 15 said their parents fret over cash, mirroring a similar proportion of mothers and fathers (92%) who said they were concerned about their finances, Halifax found.
However, the study highlighted a lack of awareness among parents about their children's concerns, with only a third (36%) of parents thinking their money problems had been picked up on by their children.
More children said they would prefer to learn about finance from their parents than from any other source, including teachers and the internet. Savings topped the list of aspects of finance they would like to know more about, followed by bank accounts (57%) and credit cards (20%).
Parents in the North East and Yorkshire were the least likely to think that their children were worrying about money, at 32%. Children in Wales were the least likely to worry about money, with less than half (47%) saying they did so.
Parents in London were most likely to think that their children worry about money at 49%. However, there was still an awareness gap in the English capital, with 72% of children there saying they worry about finances.
Richard Fearon, head of Halifax Savings, said: "As parents, we try and protect our children from the things that worry us but sometimes it can be more beneficial to talk through financial concerns as a way to help children better understand money and put things into perspective.
"We know that children are very aware of the behaviour of people around them and by having discussions about money from an early age children will be much better placed to know how to manage their money as they grow up."
More than 1,000 children and 500 parents took part in the study last month.