Staff around the country are reporting they cannot use the childcare services offered by councils for key workers.
The Scottish Police Federation (SPF) carried out a survey of its members, asking them about schooling provision during the outbreak.
More than 5,000 officers and police staff responded, with 60 per cent saying the current childcare arrangements will not help them.
Police officers have been classed as category two key workers during the Covid-19 outbreak - most healthcare professionals are considered category one.
SPF chairman David Hamilton told the PA news agency: "It's causing us significant concern.
"What is being offered by the local authorities is nowhere near good enough."
Mr Hamilton said demand for policing is likely to increase in the coming days as the virus is expected to peak.
He added: "There's a totally disparate approach across the country on it, some people have been offered schooling and others haven't.
"We're in a situation that as we approach the time of greatest need we have healthy police officers and staff who are at home because of childcare issues."
He said so far only one council, Moray, had confirmed childcare arrangements for emergency service workers over the Easter holidays.
Police Scotland Chief Constable Iain Livingstone was asked about the issue on BBC Radio Scotland's Good Morning Scotland programme.
He said: "It does concern me ... we have raised this at the highest level, at ministerial level.
"It went into the Deputy First Minister and others. I know there is lots of working getting done centrally and through local authorities but it is a monumentally challenging time.
"I know the people of Police Scotland are going to step up to the challenge and I know the public and people of Scotland are going to step up to the challenge."
Local authority umbrella body Cosla said councils are working hard to provide childcare during the lockdown.
A spokesman said: "We recognise the extreme pressures faced by all businesses and employers at this very difficult time.
"Our priority is to ensure that vital services continue as far as possible.
"Local authorities have worked tirelessly to ensure that there is provision available for the children of key workers in an extremely tight timescale.
"However, our capacity to do so needs to be established in line with public health advice."
He added: "The safety of our children, young people and staff is paramount.
"This guidance is aimed at making sure we all work together to get through this crisis while trying to minimise the impact on our society and economy.
"We recognise the value of our key partners in police who will understand the need to adhere to clear public health guidelines to protect the population."