Revd James Stevenson of St Michael and All Angels Church, Bishopston has defended the decision despite teacher Naomi Hayama, 39, teaching classes from the floor heated church hall for the last nine years.
Revd James Stevenson said: "We understand yoga is practised as a physical exercise and discipline but it's definitely a spiritual act whose roots are not Christ centred.
"We are confident we have acted legally and fairly in handling this matter but we understand why the students are upset.
"One student of the class said everyone he had spoken to had viewed it as a ridiculous decision but every church leader I've spoken to completely understands this decision.
"It is a beautiful building with under-floor heating - it's the perfect place for a yoga class and we understand that people are upset."
"We think there will be lots of people who think we are not making a very nice decision but we are trying to make the decision in the nicest way possible."
However, Ms Hayama has claimed her yoga classes are purely exercised based, despite the practice being rooted in Hinduism, Buddhism and Jainism.
Ms Hayama said: "They are trying to say it is a spiritual practise but my classes are not. I respect people who are religious but I am not. That's what attracted me to yoga - you don't have to be religious to teach it.
"My students are puzzled and outraged as well. My class is a physical exercise which is about relaxation and breathing and it's a healthy thing to do.
"The students enjoyed coming to the church and now being told they are not really welcome. Many of them have written in to the church to try and change their minds but they are being really stubborn about it.
"The decision was made without seeing my class, which is what I have a real problem with. Seeing it and deciding it's not appropriate is one thing but to do no investigation and just talk about yoga's background is another."
Teacher Naomi Hayama has until the end of February to find a new home for her classes.
