ISRO sources said 44-year old Buela N Sam of Ahmedabad entered the premises at 11 am on September 22 and was there till 3 pm after crossing two layers of security.
She was caught on the first floor when she tried to enter a meeting on Earth Observation Satellites, attended by some of the senior-most officials on campus, the sources said.
ISRO Director Deviprasad Karnik said, "an internal investigation has been initiated."
The sources said it was too early to conclude whether this was part of a larger conspiracy.
Buela had got the fake identity card from Kerala and had stayed at the ISRO official guest house at Jeevan Beemanagar, about 10 kms from the headquarters, for two days.
Police gave a different version, claiming she was caught at the entry gate itself and that there was no security breach.
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City Police Commissioner Jyotiprakash Mirji said the Central Industrial Security Force had got suspicious when Buela enquired about a conference, which was not scheduled for that day. After a preliminary enquiry, she was handed over to police.
Mirji said the woman had stayed at the ISRO guest house since September 19 by using a fake ID card.
Buela has been sent to judicial custody till October 6 on charges of criminal trespass and other offences.
She has been booked under IPC sections 471 (using as genuine a forged document), 420 (cheating) and 490 (breach of contract of service during voyage or journey).
The fake ID card showed her as an employee of the ISRO Mangalore unit where there is no such facility.
Both ISRO and the police said Buela had not got access to any crucial documents or information.
Another official said the woman had visited Kollam in Kerala to attend the last rites of her father on September 19 and arrived here the same night.
She had got the fake ID card done at a photo studio in Kollam, he said.
Police said the woman's husband, who is in the city, claimed she was mentally challenged and being treated for depression, which was being verified.