Chappell, a former Australian captain, was hit and pushed as the Indian team arrived in Bhubaneswar in the eastern state of Orissa to play a one-day international against the West Indies.
Indian cricket board vice-president Rajiv Shukla said that the 58-year-old Chappell was unhurt and had been immediately rushed into the team bus stationed outside the airport gate.
"My information is that Greg has not been hurt but this is a serious security lapse on part of the Orissa police," said Shukla, speaking from New Delhi.
"We have demanded that the state government increase security for the two teams."
The attacker, identified as Biranchi Maharana of Kalinga Sena by local officials, was arrested soon after the incident.
"I am angry with Chappell because no player from Orissa has been included in the national team," Maharana shouted to reporters before being whisked away in a police jeep.
Chappell won the coaching job for India in June 2005 and has faced close scrutiny in a cricket-mad nation desperate to see its team succeed on the international scene.
The second one-dayer will be played in neighbouring Cuttack on Wednesday. India won the first game in Nagpur on Sunday to take a 1-0 lead in the four-match series.