Citing police evidence, Andrews said on the day Haneef was arrested while trying to leave Australia, he was told by one of his brothers in India in an internet chatroom: "Nothing has been found out about you."
"Investigators consider Haneef's attempted urgent departure from Australia on a one-way ticket ... to be highly suspicious and may reflect Haneef's awareness of the conspiracy"
Kevin Andrews, immigration minister
The brother, Shoaib Haneef, told Haneef to leave Australia that day and to tell his boss that he was leaving because his wife had given birth and "do not tell them anything else", said Andrews.
"Investigators consider Haneef's attempted urgent departure from Australia on a one-way ticket for a purpose that appears to be a false pretext to be highly suspicious and may reflect Haneef's awareness of the conspiracy to plan and prepare the acts of terrorism in London and Glasgow," he added.
The minister did not say how the information was obtained, but police have said they seized Haneef's computer after his arrest on July 2, and were sifting through tens of thousands of documents.
Haneef, a junior doctor in an Australian public hospital for almost a year, returned to his wife and newborn daughter in Bangalore after prosecutors dropped a terror charge against him due to a lack of evidence.
He spent 25 days in an Australian jail on a charge of supporting the failed attacks by leaving his SIM card with a relative in Britain last year.
Haneef wants Australia to apologise for his treatment and plans to appeal against the minister's decision to revoke his visa in an Australian federal court on August 8.
Peter Russo, his lawyer, said the government should prove the allegations or stop the "campaign of innuendo and slander" against Haneef.
His cousin, Imran Siddiqui, accused the minister of "yet another desperate effort" to mislead the Australian public.
"He knows that they have nothing against Haneef and this seems just another effort by Andrews to justify his actions," said Siddiqui. "What is this protected information that [he] keeps talking about?"
A minor opposition party accused Andrews of unfairly seeking justification for ruining Haneef's life.
Andrew Bartlett, leader of the Australian Democrats, told ABC radio: "This shouldn't be about ministers seeing if they can get enough information out there to make the public sufficiently suspicious so that they'll let them get away with destroying a person's life."