The Government expects nursery, reception, year one and year six pupils to be back in primary school, and year 10 and year 12 students to their school or college, from June 1 at the earliest.
But the Labour-run West Yorkshire authority believes three of the five Government's tests have not been met.
The council's director of public health, Deborah Harkins said they were not assured that the position would change before June 1.
She said: "This means that we cannot advise our local schools that it will be safe to re-open yet.
“Test three requires us to be confident that the rate of infection is decreasing to manageable levels, but we do not currently know the impact of the changes to the lockdown restrictions announced last week.
“The fourth test is about whether we have enough testing capacity, however the full test, trace and contain programme is not yet fully in place to help manage any local outbreaks of infection.
“Finally test five is about whether we can be confident that any changes we make will not risk a second peak of infections.
"Unfortunately at this stage we cannot be confident that we could prevent the spread of the coronavirus within our nurseries, schools or colleges and then into the wider community.”
The council said schools in Calderdale which were in smaller Victorian buildings would find it difficult to conform to social distancing, smaller class sizes and increased hand washing.
A row has been raging over whether schools reopen. A handful of local authorities across England have so far advised schools against reopening more widely.
Chief executives of some academy chains have said schools must reopen soon to avoid "irreparable" damage to vulnerable children, while union bosses say more scientific evidence is needed to show it is safe.
Guidance issued by the Department for Education (DfE) last week acknowledged that young children could not be expected to remain two metres apart from each other and staff.
Instead, the Government advice said primary school class sizes should be limited to 15 pupils - and these small "consistent" groups should be kept from mixing with other pupils and staff during the day.
But the guidelines from the unions calls on head teachers to maintain social distancing in classrooms, and in movement around the school, and operate in a similar way to other workplaces.
It says: "This means that leaders must determine the numbers of pupils they admit according to maintaining social distancing of 2 metres between pupils and between pupils and school staff.
"The number of children in each class must be calculated accordingly. In most classrooms this will mean fewer than 15 children present at one time."
Speaking on Good Morning Britain, Dr Hilary Jones said that the public must get used to living without "scientific clarity".
He said: "[Education] gives those vulnerable children a chance to catch up with children from more privileged households. There's the risk of the virus, but there's also the risk of lack of education.
"We're going to have to live with this virus. We can't keep children at home forever, so at what point do we reintroduce them into school again?"
The DfE was asked to comment.