Hundreds of demonstrators rallied near the family home of Mohammed Afzal Guru in northern Indian Kashmir hours after authorities said he had been hanged.
Similar protests were held across the frontier on the Pakistani side with demonstrators burning Indian flags and shouting "Down with India".
Some 36 people, including many police, were hurt in protests near Guru's home and across Indian Kashmir as police fired into the air to disperse demonstrators but none were seriously injured, the Press Trust of India news agency reported.
Guru, 43, was hanged at Tihar Jail after President Pranab Mukherjee rejected a mercy appeal. He had been convicted of waging war against India and conspiring with the Islamist militants who attacked the parliament -- an event that brought nuclear-armed India and Pakistan to the brink of war.
"Afzal Guru was hanged at 8:00 am. All legal procedures were followed," Home Minister Sushilkumar Shinde told reporters after the execution.
India's main opposition party welcomed the hanging, but one of Guru's co-accused who was later cleared called it a travesty of justice. Human rights group Amnesty International said Guru's trial fell "considerably short" of international fair standards.
Guru had always insisted he was innocent and said he wanted to see his teenage son grow up.
Fearing a backlash over the execution of the one-time fruit merchant, authorities imposed a tight curfew in major populated areas of Indian Kashmir. A separatist conflict in the disputed Himalayan region has claimed up to 100,000 lives.
Authorities also cut off cable television and mobile Internet lines in Kashmir while India's home ministry issued an advisory to state police across the country to be on guard against any violence following the hanging.
Guru was arrested after five militants stormed the parliament in New Delhi on December 13, 2001, killing eight policemen and a gardener before security forces shot them dead. A journalist who was wounded died months later.
India alleged the militants behind the attack were supported by Pakistani intelligence, creating a tense eight-month standoff as the neighbours deployed an estimated one million troops on their borders.
India's main opposition party, the Hindu nationalist Bharatiya Janata Party, said while the execution had been delayed too long, the world now "could see India is committed to the fight against terror".
India says the death penalty is reserved for the "rarest of rare" cases and the execution came after the government hanged the sole surviving gunman from the 2008 Mumbai attacks, Pakistan-born Mohammed Ajmal Kasab, last November.
But the hanging drew bitter criticism from Muslim-majority Kashmir where leading separatist leader Mirwaiz Umar Farooq announced a four-day shutdown of the scenic region in protest.
"This execution will definitely strengthen our resolve and add a new chapter to the freedom struggle," said Farooq, chief priest at Kashmir's main mosque.
Guru had been "framed", Farooq added.
Farooq and another leading separatist leader Syed Ali Shah Geelani were taken into preventive custody, a form of detention used frequently by Indian authorities to maintain law and order.
One of Guru's co-accused, S.A.R. Geelani, a college teacher, who was also sentenced to death but later cleared, said Guru never received a fair trial.
He told AFP that Guru's family were not informed that his execution was imminent but the government said they had been notified by express mail.
Supreme Court advocate Kamini Jaiswal told local television the execution was driven by the government's desire to appear tough on militancy with 2014 polls looming and said Guru's conviction was based "on circumstantial evidence".
Guru's family said they were asking authorities to be allowed to perform his last rites inside the prison and also to be given the body.
"We have written a letter to the deputy commissioner of Baramulla district demanding Afzal's body," his cousin, Yasin Guru, told AFP.