According to Education Executive, Our Lady of Lourdes Catholic Primary School closed on Thursday for a 'teacher day' so they could have the opportunity to travel to the holy city for a four day pilgrimage.
It has been reported that parents have criticised the school for closing during term time, when parents would be fined for doing that.
An anonymous father described the situation as a "disgrace".
He said: "Nowadays parents are fined if they take their children out of school for trips or holidays, and that's something I agree with.
"But what I do find abhorrent is that a school will then fail to lead by example by closing to pupils so the teachers can swan off to Rome."
Our Lady of Lourdes teaches around 250 pupils aged three to eleven years old.
The school received the highest rating in all areas when it was visited by Ofsted in September 2014. It was described by the inspecting body as having "a strong spiritual ethos and a clear set of values [which] inform every aspect of the school's work."
The schools head teacher, Bernadette O'Shea, said the trip comes after "a successful staff pilgrimage - two years ago to Lourdes in France.
"We are an outstanding school and our faith is very important to us, as is the spirituality of both the children and the staff.
"Training days are about staff development, and as a faith school nurturing staff's spirituality is crucial."
Head teacher Bernadette O'Shea emphasised this was not a holiday and that staff had funded the excursion themselves, she said staff had a full itinerary including prayer sessions and reflective periods.
She added that parents had been told in advance about the training day, which had also been authorised by the governors of the school last year.
A spokesperson for the Archdiocese of Birmingham commented: "Catholic schools have a duty to support the spiritual development of staff, so that in turn, they are able to nurture the spiritual development of the pupils in their care.
"It is an expectation that Catholic schools devote one of their five annual staff training days for this purpose. Such opportunities may include pilgrimage or retreat experiences.
"In making a pilgrimage to Rome, staff of this outstanding school have willingly given of their own time so that they can work to strengthen the Catholic mission of the school on their return."