St Paul's Church of England Primary School in Wibsey closed on Monday when Covid-19 tests for two siblings came back as positive.
The West Yorkshire school has since advised parents of pupils to self-isolate if they or their children came into contact with the siblings.
In a statement released through Bradford Council, Headteacher Cath Palmer said: "I can confirm that, following the advice of Public Health England, I have contacted the parents of children currently attending the school to alert them to the fact that two relatives who have been attending the school have tested positive for Covid-19.
"We have followed all the correct procedures advised by Public Health England."
Ms Palmer told parents the two pupils had completely recovered.
The school is remaining closed this week while a deep clean is carried out, although vulnerable children and children of key workers are still able to attend.
Local councillor Ralph Berry told YorkshireLive: "This tells us that we are not through this crisis and that we need to be really listening to the Director of Public Heath in Bradford (Sarah Muckle).
"We need to continue to observe social distancing and be very careful. The Government message has been very confusing."
The school is not the only establishment forced to close its doors shortly after reopening - Arboretum Primary School, in Derby, was also forced to shut when seven staff members tested positive.
A spokesman for the Derby Diocesan Academy Trust confirmed to MailOnline that the school had been closed "due to a number of staff having confirmed cases of Covid-19".
Year One and Year Six pupils around the country returned to classrooms on Monday as part of a phased school reopening under Government plans to gradually ease lockdown. In many areas, secondary school pupils in years 10 and 12 will follow on June 15.
Schools are beginning to open around the country, with patchy attendance. In some areas, some schools have found a lack of demand from parents.
New safety rules include limiting contact between groups of children, staggered lunchtimes and drop-off times, no soft toys and more handwashing.
Parents will not be fined and schools will not be held to account for absences.
A poll by the National Governance Association found that three in four governors said it was unlikely that pupils would be back for a full month before the summer.