The committee oversees the work of MI5 and other security agencies
MI5 is ditching staff who lack computer skills in a programme of compulsory and voluntary redundancies.
The Intelligence and Security Committee said the service had been reviewing its staff profile and one area of concern was the level of IT skills.
MI5 director general Jonathan Evans told the committee: "I think some of the staff perhaps aren't quite the ones that we will want for the future."
It also said MI5 faced cuts because of the state of the public finances.
Patrick Mercer, chairman of Parliament's counter-terrorism sub-committee, backed the move over computer skills.
He said: "As terrorism changes, counter-terrorism officers have to adapt to keep up.
"Our enemies use every available method to attack including using technology.
"We have to be aware of the imminent threats of cyber attacks and the old generation of MI5 have to be completely comfortable using computers and the latest technology."
Mr Mercer added: "There is no room now for the 'old school tie' or recruitment from just certain Oxbridge colleges.
"We need people from all walks of life who can speak a range of languages and possess certain technical skills."
The committee oversees the work of the Security Service (MI5), Secret Intelligence Service (MI6) and the Government Communications Headquarters (GCHQ).
It reports directly to the prime minister, rather than Parliament, and its report is partially censored.
Computer security consultant Phil Robinson, who has worked with the government, said he was surprised by the move.
"I know a lot of people who are over 60 who are quite capable of using Facebook and Twitter," he said.
"A six-year-old can use them, so I'm sure a 60-year-old can."
"It's important to have computer skills in that line of work, and the UK security services are full of people who have got good computer skill-sets."
"But it's an essential part of most jobs. Just to pick out MI5 is a bit bizarre."