The university chaplain, the Very Rev Fr Sebastian Jones, said that no Catholic could remain a member of an organisation that upholds "the promotion of, and material support for, the procurement of abortions".
He added: "For a Catholic to participate in such an organisation would risk them incurring excommunication."
The students' union said it recognised its responsibility to uphold freedom of speech and to allow students to take a stance on sensitive issues.
"If students vote in favour of a position, it does not mean that students who have opposing views are censored or their views are not welcome," it said.
Cardiff University Students' Union adopted an official pro-choice stance last Thursday.
The chaplain said that Catholic students and those opposed to abortion would be unable to hold offices in societies or voice "opinions that while acceptable by civic society... are to be surprised at Cardiff University".
He likened their plight to the historical discrimination experienced by Catholics barred from holding public office until the 1880s.
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