Ms Dorries received the money following her tenure as culture secretary under Boris Johnson, but under current rules it should not have been paid.
A departing minister is entitled to three months’ salary in lieu of notice but only those under 65 are eligible.
Ms Dorries turned 65 several months before she quit as an MP following a row over her exclusion from Mr Johnson’s resignation honours list.
I’ll pay it back on Monday morning, there are no details in the email on how to do that but I will, I’m sure, find out. I was gutted
Speaking on the BBC’s Sunday With Laura Kuenssberg, the former minister said she had only seen an email about the error on Friday and promised to pay it back “on Monday morning”.
“That means now everybody knows I’m not 49,” she joked.
“I’ll pay it back on Monday morning, there are no details in the email on how to do that but I will, I’m sure, find out. I was gutted.”
As first reported by The Times, Government accounts show she received £16,876 as an exit payout following her tenure under Mr Johnson.
Labour has recently pledged to reform ministerial severance pay rules if it wins power in the election this year after it emerged nearly £1 million was spent during last year’s political turmoil.
The Opposition says it would link payouts to time spent in office so that departing ministers get a quarter of their actual earnings over the previous 12 months instead of their final annual salary.
Ministers who leave their job while under investigation for misconduct or a breach of the rules would have their severance suspended too, and quashed if the claims are upheld under the plans.
The Government has been contacted for comment.