About 28% of the college's students are from minority backgrounds
Two pupils and their teacher were asked to remove Muslim face veils on a visit to a sixth form college in Lancashire.
At an open day held in Catholic St Mary's College, Blackburn, the visitors were asked to remove their Niqab veils.
"There is a long-standing policy that people entering the site do not have their faces covered," college principal Kevin McMahon said.
The students removed their veils but the accompanying teacher declined to and left the premises, he added.
A spokesman for the Ramadhan Foundation said the women's decision to wear the veils should be recognised.
But Mr McMahon said: "Dialogue can only take place if all those in the college are prepared to participate in full communication.
"When the policy was explained to them all except one were willing to remove it.
"This lady, a member of staff at the [pupils'] school, refused, and opted to leave the premises.
"My colleague offered to arrange transport but this offer was declined."
He added the college was committed to promoting understanding between people from different backgrounds.
A spokesman for the Muslim Council of Britain said it was a "trivial issue".
About 28% of all students at the college are from minority ethnic backgrounds, according to the 2008 Ofsted report.