Premier Peter Gutwein said all workers in the sector would need to have at least one dose by January 8.
The island state, which will throw open its borders to all fully-vaccinated travellers on Wednesday, is the last Australian jurisdiction to introduce the measure.
Public Health Director Mark Veitch said the mandate would help childcare services stay open if the coronavirus spreads.
"The workers in these services are limited ... there's a required number of workers to manage specified numbers of children," he told reporters on Tuesday.
"A small loss of workers from that service can disrupt the service to quite a number of children and the parents who rely upon the sector."Â
Mr Gutwein said Tasmania's high vaccination rates and lack of community transmission held it in "extraordinarily good stead" for when borders reopen.
Tasmania has had a hard border in place with New South Wales since late July and Victoria from mid-October, and is also shut to the ACT and hotspots in other states and territories.
Under the reopening plan, travellers from high-risk jurisdictions must have returned a negative test within 72 hours before they arrive.
Mr Gutwein said more than 90 per cent of Tasmanians aged over 16 are fully vaccinated.
"While other states have opened their borders at 80 per cent, we took the very sensible decision to wait until we had 90 per cent," he said.
"And, importantly, to ensure 100 per cent of Tasmanians have had the opportunity to receive a vaccination."
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