Mr Henshaw, who is an Australian, said no reason has been given for his deportation.
"The act which went through last night in parliament... basically turns this place into a dictatorship with no right of appeal or no obvious rights of appeal," he told ABC Radio Australia.
"According to the act I do have seven days but that doesn't come into play at all."
He says his lawyers have applied for a stay of the deportation order.
The Nauruan government says it has the right to sack and appoint who it likes, after facing criticism for sacking two Australian judicial figures.
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Nauru's government is under pressure to explain why it sacked its chief justice Geoffrey Eames and only magistrate Peter Law, both Australian citizens.
In a statement on Friday, Nauru President Baron Waqa said his tiny island nation had the same rights as Australia to make decisions on who's allowed to work in the country and hold key positions.
Mr Waqa denied the dismissals were politically motivated and suggested the two had engaged in "unacceptable conduct that compromised their roles".
"There have been clear conflicts of interest and disregard for the laws of our nation," he said.
"It is ironic that we are being criticised for demanding integrity and honesty and for making normal decisions every government makes around the appointment of key personnel."
Mr Waqa also rejected "insinuations" that the rule of law was not respected in his nation.
