Some maxed-out parents are using their children's bank accounts to secure additional credit in the form of quick loans, often obtained by text message at exorbitant interest rates.
Just under half of those account holders were under 13 years of age.
"It's basically using their children's identity, and it can leave a mark on their credit rating," Swedbank spokeswoman Kristi Roots told EPL.
SEB's Triin Messimaa said it has also noticed sums of money far exceeding usual gifts and allowances accruing on kids' accounts.
Two popular quick lenders, Credit24 and Raha24, told the papers the information came as a surprise to them and that such a scheme was possible only if the lender authorizes a third party account.
The major commercial banks have long criticized express lenders, saying they leave a black mark on the entire financial services industry.
A total of 45,000 to 50,000 adults in Estonia are considered to be in difficulty repaying loans to express lenders. The total number of borrowers has been estimated at 130,000-180,000.