Naz Shah, shadow women and equalities minister and MP for Bradford West, said she withdrew from the event after she learned that the far-right commentator would be on the panel.
Protests were held outside the event on Thursday evening – where Ms Hopkins was joined by controversial journalist Toby Young and former Conservative MP Ann Widdecombe.
A 21-year-old man was arrested on suspicion of common assault during the protests after liquid, which was believed to be a drink, was thrown and hit a man and a woman.
Genevieve Athis, president of the Oxford Union, said she was “very disappointed” that Ms Shah dropped out of the debate “at such a late stage.”
She told student newspaper Cherwell: “I think it is a great shame that instead of debating Ms Hopkins in our chamber Ms Shah has decided to not participate altogether and I am sure that many of our members will also be deeply disappointed by this.”
Ms Hopkins said on Twitter that it was ironic that the MP pulled out of a no platforming debate.
In a statement sent to The Independent, Ms Shah said: “I believe in free speech, the right to hold contrasting beliefs, to challenge bigoted views through debate and dialogue.
"However, with everything including freedom of speech, there is always a line to be drawn and I draw the line at those who use racism to dehumanise people, especially those from minority groups.”
She added: “Speaking at the Oxford Union is supposed to be an honour and a privilege. When such platforms become acceptable places for those that try to divide communities and drive hatred towards certain minorities, then such a privilege and honour is not for me."
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