A message to parents from Westerton Primary Academy in Tingley read: "We have a confirmed case of Covid-19 in Reception.
"As a precautionary measure, having consulted Public Health England, we are closing Foundation Stage and Nursery from 11am for a deep clean."
"Foundation Stage children will need to be collected from their class through the gate on Westerton Road.
"Thank you for your understanding."
An answer phone message on the school's telephone number said that the rest of the school would remain open.
But at lunchtime on Monday, Morley and Outwood MP Andrea Jenkyns said she has spoken to the school and that the case was only "highly likely".
She said: "I've spoken with Westerton Primary School to offer my help & support regarding the 'highly likely' #coronavirus case of one of their Reception aged pupils.
"The school have explained the situation & I know the school are doing a fantastic job & doing everything possible including a deep clean."
An answerphone message left on the school phone on Tuesday said the child was only "suspected" of having Covid-19.
A Leeds City Council spokesman said: “As a council we take the confidentiality of information about children, families and staff very seriously.
"Consequently, we will not be providing information about individuals or commentary on their circumstances.
"Leeds City Council is working with the Government and Public Health England to follow national guidance and NHS advice for schools.
"This guidance currently advises that staff, young people and children should stay at home if they are unwell with a new, continuous cough or a high temperature to avoid spreading infection to others.
"Otherwise they should attend education or work as normal.
"This is a fast changing and evolving situation and we will continue to work closely with schools and liaise with Public Health England to ensure we follow advice, prevent the spread of the virus and take all the precautions necessary to protect those who are most vulnerable to this disease.”