The police crackdown comes weeks after Mr Singh's supporters stormed a police station, demanding the release of an aide who had been arrested.
On Saturday, police declared Mr Singh "a fugitive" and launched a state-wide search for him. Traffic blockades were set up across the state to check vehicles.
Local media reported that Mr Singh travelled in a cavalcade and dodged the police near the Shahkot-Mehatpur area in Jalandhar district after a dramatic chase.
The chase through villages was live-streamed by some of his associates, the Times of India newspaper reported, adding that they also uploaded videos on social media urging supporters to gather near Jalandhar.
One of the videos showed the preacher's convoy being stopped at a check post near Jalandhar and then being followed by several police vehicles.
Mr Singh's uncle Harjit Singh, who was part of the convoy and surrendered to police on Sunday night, told the Indian Express newspaper that his nephew had been in the car with him as they were heading to Moga district in Punjab.
He said that they were alerted about a "heavy deployment of armed forces" and so they changed route and Mr Singh switched to another car.
On Sunday, a top police official told ANI news agency that the preacher had managed to escape after "he had been chased for 20-25km (12-15 miles)".
The police have marched through the streets in several areas of Punjab to "instil confidence in the public" and to urge them to maintain law and order in the state. (BBC)