A protest by the traders last week turned violent
Shopkeepers say the moves will affect the livelihoods of 500,000 people.
Security is tight on the streets of Delhi, and police contingents were seen outside some of the city's major markets early in the morning.
The Supreme Court has ordered the authorities to seek help from the police to carry out the drive.
Major city markets are expected to remain closed on Tuesday. Several private and public schools have also decided to remain closed fearing violence on the streets.
Some protestors were reported to have attacked passenger buses in the north of the capital.
Angry traders held a three-day strike last week, closing most of the city's shops. In September four people died as protests turned violent.
A total of 44,000 illegal businesses have been targeted during the controversial ongoing drive.
'Dagger'
On Monday, the Supreme Court dismissed petitions filed by the federal government and Delhi's local government.
The petitions had said that the closures could threaten law and order in Delhi.
"No one can be permitted to place a dagger at the government's neck and seek relief. No one can be permitted to hold the city and its law-abiding citizens to ransom," the Supreme Court order said.
"It is the obligation of governments to ensure compliance of the orders of this court."
The drive against illegal businesses in residential areas began last year after the Supreme Court said a ban on such shops had to be enforced.
Protests across Delhi have since become widespread.
Traders say municipal authorities often take money from the poor and the middle-class in return for turning a blind eye to illegal constructions or encroachments on public land.
Angry traders continued to protest against the Supreme Court's order in favour of resuming the sealing drive in New Delhi. They damaged public property and blocked traffic during the protest.

Police halted over 1,500 traders from various part of the city who were vandalising public transport by blocking and pelting stones on the roads after the SC's order to resume the drive.

According to CNN-IBN, the drive will affect about 5,40,000 shops and 27,00,000 traders across the city. Praveen Khandelwal, secretary general of the Confederation of All India Traders (CAIT), said that the resumption of the drive is a complete breakdown of the government and administration. So, they had to take extreme steps to oppose the drive.

The traders protested from all over the city including Kamla Nagar in North Delhi, Mayur Vihar, Vikas Marg, Seelampur in East Delhi, Green Park, South Extension, Lajpat Nagar in South Delhi, Rajouri Garden, Rohini in West Delhi and Karol Bagh in Central Delhi.

Most of the schools in New Delhi remained closed today, and the sealing drive was halted. The Group of Ministers, headed by Shivraj Patil are planning to meet with SC's monitoring committee to work out the sealing schedule in the capital.