The Indigo airline Airbus A320 plane was landing in the Indian capital from the tourist resort state of Goa when the emergency was declared.
An airport official said the cause of the alert was a passenger "causing trouble," while some local media reported that the man claimed to be carrying a knife.
Airports across India have been on maximum alert since the deadly Mumbai siege in late November, but security officials said Sunday's incident was not a militant attack.
One man speaking to the NDTV television network from onboard the plane said that it was surrounded by armed security personnel.
"Outside we can see a lot of commandos with guns all crouched around," he said. "Inside the passengers are all calm, everything inside is normal but passengers are getting restless."
Passengers later began to disembark the aircraft.