The move had been expected since last week, when Amazon said it wouldn't settle with the FTC over the charges. Amazon said in a letter to the FTC last week that it had already refunded money to parents who complained and was prepared to go to court.
On Thursday Amazon said its statements in the letter still apply and did not comment further.
The dispute is over in-app charges in children's games on Kindle devices, where it can sometimes be difficult to differentiate whether users are spending virtual or real currency to acquire virtual items. When it introduced in-app charges in 2011, a password was not required to make a purchase. That changed in 2012, when Amazon required a password for charges over $20. In 2013, the company updated password protection again, but in a way that allowed windows of time where children could still make purchases, according to the FTC complaint.
One woman cited in the complaint said her daughter racked up $358.42 in charges while playing a game.
The lawsuit seeks a court order requiring refunds to consumers for unauthorized charges. It also seeks to ban Amazon from billing account holders for in-app charges made without their consent.
The FTC settled with Apple over a similar matter for $32.5 million in January.
Apple complained at the time. CEO Tim Cook explained to employees in a memo that the settlement did not require the company to do anything it wasn't doing already but he added that it "smacked of double jeopardy" because Apple had already settled a similar class-action lawsuit in which it agreed to refunds.
Amazon said last week its parental controls already go beyond what the FTC required from Apple as part of the settlement.
The complaint was filed in the U.S. District Court for the Western District of Washington.
Amazon's shares slipped 35 cents to $329.62 in afternoon trading.