The minister around 5.15 PM called police saying that some youths in a car were following her vehicle, a senior police officer said.
Acting on the complaint, police intercepted the car, in which the four youths were travelling.
The four students, in the age group of 18-19 years, have been detained at Chanakyapuri police station.
"Their medical examination has confirmed the presence of alcohol in their blood. They were returning from a friend's birthday party in south Delhi and were roaming in the area for fun," he said.
Further details in the matter are awaited.