Schools should not reopen unless key measures are in place to stop the spread of coronavirus, unions have warned.
The Trades Union Congress (TUC) is urging ministers to work closely with unions to agree a way forward.
England's Department for Education said it would follow scientific advice about the "right time" to reopen schools.
Schools across the UK closed in the last week of March as part of the lockdown measures to prevent the virus spreading.
Prime Minister Boris Johnson will give details on Sunday of his "roadmap" to get the UK out of lockdown.
Speaking to BBC Radio 4's Today programme, Mr Drakeford added: "We're not going to be reopening schools in Wales in the next three weeks, or indeed in June."
Unions, including the National Association of Headteachers (NAHT) and the National Education Union (NEU), have called for "clear, scientific published evidence" that schools are safe to re-open.
In a joint statement sent to UK Education Secretary Gavin Williamson, they said there should be no increase in pupil numbers until a national test, track and trace scheme has been fully rolled out.
The government's three-pronged coronavirus strategy is being rolled out in various stages, with the NHS contact-tracing smartphone app currently being trialled on the Isle of Wight before a UK-wide expansion.
They have called for extra resources for deep cleaning, personal protective equipment (PPE) and local powers to close schools if there is an outbreak of the virus in a particular area.
Some of the other "essential" measures unions said must be in place before pupils return, include:
- Safety and welfare of pupils and staff as the paramount principle
- A national Covid-19 education taskforce with government, unions and education stakeholders to agree statutory guidance for safe reopening
- Consideration of the specific needs of vulnerable students and families facing financial hardship
Frances O'Grady, general secretary of the TUC which published the statement, said: "Parents and staff need full confidence that schools will be safe before any pupils return."
She urged No 10 to "work closely" with unions to "agree a plan that meets the tests we have set out", adding the best way to do this would be through a "national taskforce" between "government, unions and education stakeholders".
A spokeswoman for England's Department for Education said Mr Williamson has not set a date for schools reopening, and the department would ensure the education sector has "sufficient notice to plan and prepare" for schools, nurseries and colleges to return.
"Schools will remain closed, except for children of critical workers and vulnerable children, until the scientific advice indicates it is the right time to re-open and the five tests set out by government to beat this virus have been met," she added.
Health Secretary Matt Hancock, meanwhile, said pupils will only be allowed to return to school when it is safe to do so.
It follows a warning by the British Irish Group of Teacher Unions of the "very real risk of creating a spike in the transmission of the virus by a premature opening of schools".
Labour's shadow education secretary Rebecca Long-Bailey called on the government to "take heed of the tests set out today by trade unions and commit to not opening schools unless they have been met".
Last week at the Downing Street daily briefing, NHS England's national medical director Prof Stephen Powis said the "science is still evolving" on how much children contribute toward virus spread.
It comes as the public was urged to be "realistic" about the easing of lockdown measures, as a further 626 coronavirus deaths were confirmed on Friday, taking the UK total to 31,241.
Leading the No 10 news conference on Friday, Environment Secretary George Eustice said there would be "no dramatic overnight change" and the government would be "very, very cautious as we loosen the restrictions we have".
Meanwhile, the government announced 97,029 tests had been delivered in the 24 hours to 09:00 BST on Friday, just shy of the 100,000 target Mr Hancock set for the end of April.