One parent of a pupil at the school, who wished to remain anonymous, said that their child had witnessed children being sick in the corridors.
The father also said that a teacher told his child that "hundreds of students" has been taken ill.
On Sunday evening, the school had issued advice to parents saying that the school would be open as usual, however, it has since taken the decision to close tomorrow and Wednesday.
This is due to the spread of Norovirus in the school "reaching a point today" that required a full deep clean.
In a letter to parents Christopher Walsh, principal of Boston Spa Academy, said "As you will likely be aware, across Leeds, the Norovirus is currently rife and is impacting on children and adults across the city.
"At Boston Spa Academy, we have been monitoring the situation with our own staff and students very carefully.
"We have reached a point today where we now believe that the virus is having such an impact on our student and staff population that in order to stop the spread of the virus, a full ‘deep clean’ of our premises is required.
"This afternoon I have been in contact with a professional cleaning company who will be attending our site tomorrow and Wednesday in order to complete the ‘deep clean’.
"This clean will involve fully disinfecting all floors, walls and surfaces in order to ensure that any trace of the virus is removed.
"As a result, I am writing to inform you today that Boston Spa Academy will be closed to all staff and students on Tuesday 10 and Wednesday 11 December 2019.
"Following the deep clean, it is our hope that the academy will reopen on Thursday 12 December 2019.
"If for any reason this cannot be the case, we will advise all parents via text message and post updates on our school website. In the event that you believe your child has the Norovirus, please follow professional advice in keeping your child at home for 48 hours following their last episode of illness.
"In addition, we would like to remind you that if anyone in your family exhibits symptoms, it is always advisable to seek the advice of a health professional or GP where you have any concerns at all.
"We have re-scheduled the Christmas Concert for Monday 16 December. I do very much hope this date works for all the students and their families. We have been looking forward to it.
"We are grateful for the support and understanding of all of our families during this particularly unprecedented period and we hope that anyone that has been affected feels better soon."
The Farnley Academy, Richmond Hill Academy and The Morley Academy are expected to reopen on Tuesday 9.
However, a message on the schools' websites said that parents will be notified by text message if the schools cannot reopen as planned.
Ryecroft Academy will remain closed on Tuesday.
What should I do if my child has symptoms of the Norovirus?
If your child is displaying symptoms of the Norovirus, such as diarrhoea or vomiting, you are advised to keep them at home for 48 hours following their last episode of illness.
stay at home and get plenty of rest
drink lots of fluids, such as water or squash – take small sips if you feel sick
carry on breast or bottle feeding your baby – if they're being sick, try giving small feeds more often than usual
give babies on formula or solid foods small sips of water between feeds
eat when you feel able to – you don't need to eat or avoid any specific foods
take paracetamol if you're in discomfort – check the leaflet before giving it to your child
do not have fruit juice or fizzy drinks – they can make diarrhoea worse
do not make baby formula weaker – use it at its usual strength
do not give children under 12 medicine to stop diarrhoea
do not give aspirin to children under 16
stay off school or work until the symptoms have stopped for two days. Also avoid visiting anyone in hospital during this time.