Ms Vetterlein, 25, a restaurant assistant manager, fought the Kent seat at the general election, when she took 9,858 votes.
The Tories have picked the former whip, Jacqui Lait, as their candidate. Ms Lait was the first female Tory whip and lost her Hastings and Rye seat on 1 May.
Mr Merchant, 46, who is married, spoke of his desire to shield his family and friends from "intensive and continued intrusion" when he stepped down as Beckenham MP two weeks ago after newspaper claims about a relationship with 18-year-old Anna Cox.
He subsequently admitted to the affair in newspaper articles.