"The intensity of the smog issue that has wide implications for human health calls for concerted efforts to take on this challenge," Mr Sharif said.
He posted a copy of the letter on Twitter, also tagging Delhi Chief Minister Arvind Kejriwal.
In reply, Punjab Chief Minister Amarinder Singh's media advisor Raveen Thukral tweeted "@Capt_amarinder is extremely concerned about the issue and is actively pursuing it with the Indian government. He expects early resolution of the matter. He is, however, yet to receive the letter from @CM Shehbaz @GovtOfPunjab and will reply to it at suitable time."
In the letter, Mr Sharif said that since last year, the people of both the Pakistani and Indian Punjabs were facing the problem of smog during the months of October and November.
This year the problem has become more aggravated and widespread, he said.
He wrote that smog has an adverse impact on public health, especially on the elderly and children, on agriculture in the form of delayed sowing of wheat, damage to potato and other crops and also causes traffic accidents.
The phenomenon has now assumed regional proportions and it engulfs the areas from New Delhi to Lahore and beyond, he said.
He wrote that the problem is essentially scientific and economic and can not be tackled through other means. "I firmly believe that it is in the interest of people of both Punjabs to make a collective efforts towards identifying technologies and business methods that may
eliminate the need to burn rice stubble and help control smog formation," he said.
I will like to invite you for entering into a regional cooperation arrangement to tackle the issue of smog as well as environmental pollution, he wrote.
Recently, Mr Kejriwal and Haryana Chief Minister Manohar Lal Khattar had confabulations to tackle the problem of smog.