General Bajwa did not attend the Kartarpur Corridor's opening ceremony apparently to avoid any controversy.
The chief minister also said the development raised concern over the security threat to Punjab and India as a whole.
Pakistan Prime Minister Imran Khan last week announced that no fee would be charged from the pilgrims on the opening day of the corridor and on Guru Nanak's 550th birth anniversary.
The year 2019 marks the 550th birth anniversary year of Sikhism founder Guru Nanak Dev, whose birthplace Sri Nankana Sahib is in Pakistan.
"Nationalism in its strident form is inseparable from the desire for power. It is an 'ideological poison' that has no hesitation in transcending and transgressing individual rights," he said.
The fine for violation of the rule is Rs 4,000 under the amended Motor Vehicle Act
The number of pilgrims had also increased compared to last year
Mukherjee asked all to endeavour to follow the Guru's profound teachings and work to strengthen the bonds of togetherness