This is the first time the New Jersey gambling regulators have had to issue a fine for underage internet gambling, although Caesars Entertainment was penalised for accepting illegal bets in September 2018.
The Division of Gaming Enforcement announced that Rush Street's offences had begun in November 2016 and run through until January 2018.
The wagers were allowed because of a software defect which did not accurately pick up birthdates.
Thirteen individuals between the ages of 18 and 20 had been able to create accounts and stake bets. Within this period of time, almost $5k was staked.
A Rush Street statement said: "We take this matter very seriously. As soon as our team discovered the misconfiguration, we self-reported it to the gaming commission and took immediate action to correct and prevent recurrence."