The holy site is at the centre of a decades-old sectarian conflict.
More than 200 slogan-shouting activists of the World Hindu Council broke past security officers to storm into the domestic airport in the central city of Indore in Madhya Pradesh state on Wednesday, said local administrator Vivek Agarwal.
The mob smashed the VIP lounge and some of them sprawled on to the tarmac, preventing a New Delhi-bound flight of the private Jet Airways from taking off for an hour.
Police beat them back with bamboo truncheons and arrested 40 people. Airport operations were later resumed, said Agarwal.
The attack on Tuesday at a Hindu shrine complex in Ayodhya - a site considered holy by both Hindus and Muslims - left all six assailants dead and wounded three security guards.
An attack on the Ayodhya holy
site left six dead, three injured
One of the attackers blew himself up in a vehicle, tearing a hole in iron railings encircling the complex and allowing the five other attackers to enter the complex where they died in a gunfight with the guards, officials said.
Hindu nationalists blamed the attack on Pakistan-backed Muslim fighters and called for protests, while officials tightened security nationwide to deter clashes between majority Hindus and Muslims, which make up about 12% of the more than 1 billion population.
In New Delhi, police used teargas and water cannons to disperse hundreds of Hindu nationalists who shouted anti-government slogans near the parliament building, led by Lal Krishna Advani, head of the main opposition Bharatiya Janata Party. No one was hurt.