The arrest took place ahead of a planned demonstration against the country's electoral authority.
"Abhijeet has been arrested by the Delhi Police! The government is so afraid of young people waving the national flag," the "cockroach party" wrote in a social media post.
The movement, together with the opposition, has expressed dissatisfaction with a controversial change to the electoral roll and is demanding that election chief Gyanesh Kumar resign.
The change has prevented millions of eligible Indians from voting, according to the opposition.
Dipke was detained upon arriving at New Delhi airport less than a week ago.