The minister was appearing on the BBC's Question Time programme when he questioned another panellist who said her teachers taught "real values".
Cristina Odone, who went to a Catholic school, said some of her best teachers were at the faith school prompting Mr Hunt to question "These were all nuns, weren't they?"
It appeared the MP was questioning whether nuns made good teachers because many did not have a formal teaching degree.
When challenged on his comments by Ms Odone he said: "I know about your religious schooling and there's a difference I think between a state education system having qualified teachers in the classroom."
Sister Mary J Martin inspects schools in the Diocese of Westminster and told Premier's News Hour every teaching sister is qualified.
She said: "I am surprised at his ignorance. For somebody who is the Shadow Secretary of State for Education I would have thought he might have had a better understanding of the place that religious people have played in education in this country."
The Conservative member for Bournemouth West, Branksome East and Alderney, Conor Burns MP, said on Twitter: "Absolutely shocking, sneering comments by Tristram Hunt about Catholic schools and nuns. I was educated by Brothers. Gave lives of service"
Whilst Nadine Dorries, Conservative member for Mid Bedfordshire, said: "Tristram Hunt's sneering down his nose at Cristina because she is a Catholic was bang out of order - good rebuttal".
Mr Hunt responded to the row by posting a message on Twitter stating: "On BBC QT I was trying to make a generalised point about the use of unqualified teachers in schools. I obviously meant no offence to nuns."
Sister Mary J Martin speaks to Premier's Antony Bushfield