Jan was in a high-security gallery of top officials and ministers when he hurled a shoe at Chief Minister Omar Abdullah during the ceremony at a soccer stadium.
He also threw a black flag toward Abdullah while shouting, "We want freedom." Neither item hit Abdullah.
Jan was immediately arrested and authorities later said he was mentally unstable and had been suspended from work in May.
"It was a major security breach and we're probing how he managed to sit in the top officials gallery," said a police officer on condition of anonymity as he was not authorized to speak with media.
The officer said 15 police were suspended for lax security that allowed Jan to enter the stadium.
After his arrest, thousands of supporters shouted pro-independence slogans outside Jan's house and showered flowers on his wife as young men played musical instruments, local newspapers reported Monday.
Anti-India sentiment runs deep in Kashmir -- the Himalayan region divided between predominantly Hindu India and Muslim-majority Pakistan but claimed in full by both. Most people favor independence from India or a merger with Pakistan.
Jan's brother, Sanaullah Jan, accused authorities of lying when they said Jan was mentally unwell and had been suspended. "He is very sensitive and felt sad over the killings in the (Kashmir) valley," Sanaullah Jan was quoted as saying by the English-language Greater Kashmir daily newspaper.
Following his arrest, Jan was hospitalized later Sunday after he became sick, the officer said.
On Monday, Jan again shouted pro-independence slogans at the hospital and told reporters he wanted to meet Abdullah. "I'll expose all the lies of state police," he said.
The recent unrest in Indian Kashmir has been reminiscent of the late 1980s, when protests against New Delhi's rule sparked an Islamic insurgency that has so far killed more than 68,000 people, mostly civilians.
Separatists says they will continue protesting during the current Muslim fasting month of Ramadan.
On Monday, thousands of armed police and paramilitary soldiers patrolled nearly deserted streets in Srinagar -- the main city in the region -- and other major towns and enforced a strict curfew in most of the region. Troops laid razor wire and erected steel barricades to block access to downtown.