The activists of BJP's Mahila Morcha marched from party headquarters on Ashoka Road to Gandhi's 10-Janpath residence.
They broke the barricades near Ms Gandhi's residence, but were prevented from moving ahead.
However, the protesters, numbering around 75, were detained and taken to a nearby police station.
BJP supporters were stopped by police on Saturday near the Parliament House when they tried to take out a candlelight march towards India Gate to protest against the rape of the girl.
Police had arrested a number of protesters, including Delhi BJP Chief Vijay Goel, but later released them.
The five-year-old girl was brutally raped and assaulted allegedly by her neighbour while being held captive and starved for two days in east Delhi's Gandhi Nagar. She also contracted infection from foreign objects inserted in her body.