The Speaker announced the clerks, who advise him on conduct and constitutional issues, would also no longer wear wing collars and white tie.
Conservative Sir Gerald Howarth said the tradition of wearing wigs went back "several centuries".
But Mr Bercow said there was an even older tradition of not wearing wigs.
He announced the changes on Monday, but added that clerks would keep part of their garb - black gowns, to signify they are experts on procedure and constitutional issues.
Mr Bercow said changes to clothing and headgear represented the "overwhelming view" of clerks themselves.
They would "convey to the public a marginally less stuffy and forbidding image of this chamber at work".
But Sir Gerald, MP for Aldershot, raised a point of order, telling the Commons: "I was surprised by [the] statement, which had the sort of appearance of an executive order."
He added that traditional clerks' dress was "key to the dignity of the House" and had been so "for several centuries", adding that MPs "should discuss this".
Mr Bercow replied that it was "a matter that can properly be decided by the Speaker", adding that the House of Commons Commission had approved the changes, which clerks themselves had suggested.
He said that, if one went back more than a "couple of hundred years", the situation was different from that presented by Sir Gerald, and that "several centuries ago", clerks "did not wear wigs".
Mr Bercow has refrained from wearing a wig himself in the Commons since becoming Speaker in 2009, as did his predecessors Michael Martin and Betty Boothroyd.

One Good Samaritan gifted £600 and another gave Sue Percival £180 following the burglary at her home at Tonypandy in Rhondda Cynon Taff.
Her British Gas colleagues also raised £150 so she and her daughter were able to replace stolen goods like a laptop and three Android tablets.
"Thanks to everyone. We have replaced everything " she said.
"They have been so kind."
The man who donated £600 wishes to remain anonymous and another set up a fundraising page after South Wales Police put out a plea for information following the burglary on Wednesday between 07:30 and 11:30 GMT.
Ms Percival's grandchildren and daughter, Steph Summers, discovered the theft.
Four-year-old Tristan, the first in the house, told her: "Mum, Santa's been. All the presents are open."
Ms Percival said being a victim of burglary had been "devastating" as she felt it was an "invasion of privacy".
She said she had not wanted to leave her home since the incident.
She said neighbours had been supportive, giving her the confidence to go shopping to replace the stolen presents.
John Bercow has defended the decision that Commons clerks will no longer have to wear wigs, after one MP likened the move to an "executive order".
[NEXT_CONCEPT]
A grandmother has thanked well wishers who have saved her family's Christmas after a burglar stole £900 in presents.