Sena corporator, Rajul Patel, wearing a black sari, and two others were picked up while trying to make way into the Bhaidas Hall in suburban Vile Parle without proper invite, police said.
The trio has been detained and taken to nearby police station, they said.
Shops in both Vile Parle and Ghatkopar areas remained closed, police said, adding several trouble makers were detained last night as a preventive measure.
This is Rahul's maiden visit to the financial capital after he became the AICC General Secretary.
Hundreds of policemen are keeping vigil at the Vile Parle railway station, bus stops and the road leading to the venue.The entire road leading to the venue and across the city was dotted with posters that read - 'Fight an election, become a leader.'
Rahul Gandhi landed at the Santa Cruz Old Airport in Juhu at about 11.20 a.m. and drove to the Bhaidas Hall, barely a kilometre away, where he was scheduled to address 1,100 college students and youth.
Waiting to receive him were Chief Minister Ashok Chavan, Mumbai Pradesh Congress Committee office-bearers, local elected representatives and other prominent persons.
There were heavy security arrangements that saw traffic being stopped in and around the posh Juhu-Vile Parle area.
Despite the Shiv Sena's directives to its activists to greet him with black flags because he had "insulted" Marathi people and Maharashtra, security personnel ensured that there was not a single pennant visible.
The Mumbai Police efforts were supplemented by commandos of the National Security Guard (NSG), Rapid Action Force and other forces.
In the afternoon, Rahul will go to Ghatkopar, the north-eastern part of Mumbai where the Ramabai Ambedkar Nagar slums are located.
He will garland a statue of Bharat Ratna Babasaheb Ambedkar there, pay homage and then interact with select slum youths.
A spokesperson said both the meetings were organised keeping in mind Rahul Gandhi's desire to meet youth and students from different strata of society.
A couple of kilometres from Bhaidas Hall, a group of women activists led by Shiv Sena corporator Rajul Patel attempted to break the security barricades but they were whisked off to the police station and put under detention.
Violating prohibitory orders, Shiv Sainiks had also gathered in large groups in Andheri, Vile Parle, Jogeshwari and Ghatkopar.
After his brief visit, lasting just about four hours, Rahul Gandhi is scheduled to go to Pondicherry.