The reward of Rs 1 lakh was announced on Sidhu, Jugraj Singh, Gurjot Singh and Gurjant Singh who hoisted flags at the Red Fort or involved in the act, according to police.
The prime minister's remarks come amid ongoing protests by thousands of farmers, mostly from Haryana, Punjab and Uttar Pradesh, at several border points in Delhi.
Sidhu was present at the Red Fort when a religious flag and a farmer flag were put at the flagpole at the historic monument, triggering massive outrage.
The premises of the historic monument was vandalized as the protesters went on a rampage destroying checking machines, ticket counters, furniture, and everything that came in their way.
The Union Minister said that sometimes in a way it seems that these people who have been defeated in the elections are all gathering and trying to spoil the atmosphere in the country.
He was apprised by security personnel about the damage done to the structure and the ticket counters and how the protesters had barged into the monument on Tuesday.
