A Department of Immigration spokeswoman has told AAP the unaccompanied minors are all aged between 15 and 18.
Nine were in community detention in Victoria while the remaining teenager has gone missing from WA.
"The Department of Immigration can confirm 10 children have absconded," the spokeswoman said.
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She said the Red Cross was the contracted service provider for community detention.
Seven other unaccompanied minors are in community detention in Victoria and WA.
There are fears that the teenagers may have been trafficked.
Liberal Senate Leader Eric Abetz said the Labor government must explain how this happened.
"Why is their system failing yet again?" Senator Abetz told Canberra reporters on Tuesday.
Australian Greens senator Bob Brown said the news was worrying.
"It's very concerning," he said.
Senior Labor left figure senator Doug Cameron said the incident should not be a reflection on the merits of community detention.
"What I've seen of community detention in Australia and around the world is that it works, it's cost-effective and the most humane way to deal with refugees," he told reporters.
A spokeswoman for the Red Cross told AAP the charity was not responsible for the security of asylum seekers but was involved in providing housing, support services and English lessons.
She said the security of asylum seekers in detention was a matter for the department.
