Nayyar predicted that the entire province will fall to Taliban within the next few months.
"I also see there will be pressures by Taliban in other provinces and Pakistan is going to go back to the dark ages," he said.
The deal has also raised fears among the US and its Western allies that the valley will turn into a sanctuary for fighters from across the border in Afghanistan.
Pakistan's government lost control in Swat after Maulana Fazlullah, a local Muslim leader, launched a campaign to enforce sharia there.
During the government's battle against the Taliban in Swat, hundreds were killed, schools were bombed and tens of thousands of people fled their homes.
Zardari had referred the deal to Pakistan's parliament, which voted on Monday to compel him to sign the deal.
Legislators from the Muttahida Qaumi Movement, a party based in the southern city of Karachi that has a strong anti-Taliban stance, walked out of the parliament session before the vote.
"We can't accept Islamic law at gunpoint," Farooq Sattar, a party leader, said.
But despite the boycott, Pakistan's parliament voted unanimously to adopt a resolution urging Zardari to sign the deal and many hope the deal will help bring peace.
"It is hoped that those who wanted this law in Swat will now surrender their arms and also bring the peace"
Rehman Malik, Pakistani interior minister
"God willing it will have a positive impact on the situation in Swat," Rehman Malik, Pakistan's interior ministry chief, said.
"It is hoped that those who wanted this law in Swat will now surrender their arms and also bring the peace."
Al Jazeera's Kamal Hyder, reporting from Islamabad, said many believe the government's decision merely represents the will of the people.
"There will be people who say this was giving into the demands of the Taliban in Swat, but other people will tell you that there has been a precedence for sharia law, that before Swat was amalgamated into Pakistan, the place was governed by sharia," he said.
"So in the interest of peace, the political parties in power have indeed made a dramatic move and supported the will of the people of Swat."
Amir Izzat Khan, a spokesman for Sufi Mohammad, a pro-Taliban Muslim leader who helped mediate the agreement, said that the deal would allow peace in Swat.
"We will make all-out efforts to establish peace in the region. The Taliban have disarmed themselves and those who have not yet disarmed will do so soon," Izzat Khan said.
Muslim Khan, a Pakistani Taliban spokesman, said that, with the deal in place, "there will be no need to fire a bullet".
"Women will not be allowed either to go to jobs or markets because we do not want to make them show-pieces," he said.
Khan also said that the Taliban wanted to introduce an "Islamic syllabus" at schools.
Even without the president's approval, judges trained in Islamic law had begun hearing cases in Swat, and witnesses say Taliban fighters effectively control of much of the region.
Islamic courts have been operating in Swat since last month, but Swat residents appear to still have recourse to appeal courts under the federal judicial system, a mixture of colonial British law and sharia regulations.
Earlier in April, a video showing a veiled woman being flogged in public provoked widespread criticism of the deal.