The ruling came after a parent complained that the terms discriminated against separated, step or gay parents.
Peter Goringe of the Office of the Schools Adjudicator agreed the words were in breach of the admissions code and made Holy Ghost Catholic Primary School in Wandsworth, south London, change their entry forms.
Hundreds of schools belonging to the Catholic Education Service have already replaced mother and father on applications with Parent 1 and Parent 2.
Mr Goringe said: “In the absence of any clarification of the term parent, the use of the words mother and father might, as the objector suggests, be taken to imply that the school is restricting its definition.”
But critics last night rounded on the move.
Chris McGovern, chairman of the Campaign For Real Education, warned that we are capitulating to politically-correct fascism.
He said: “To ensure fairness, we should not be placing mother and father on a list of forbidden words.
“We should be accommodating these cherished foundation stones of our civilisation within the admissions system.
“The decision to remove them is profoundly undemocratic and illiberal and is a capitulation to a form of politically-correct fascism.”
Professor Alan Smithers, director of the centre for education and employment research at Buckingham University, said that it was part of a trend in which arrangements that worked perfectly well for the majority were being overturned for fear of offending a small minority.
He added: “Our society is based on families and the great majority have a father and a mother.
“If there is only one parent, only fill in that bit of the form.”
Parents collecting their children at the school yesterday were astonished.
One mother, from Balham, who has a six-year-old daughter, said: “You need a mother and father to conceive a child, if not then you’re not the child’s parents.
“We’re a Catholic school, I don’t see why it has been changed.”
Another parent said: “I find it sad the amount of money that the school will have to spend on this, they should spend it on making the children happy instead.”
A spokesman for the Catholic Education Service said: “We expect all Catholic schools to comply with the School Admission Code.”