Israel currently holds hundreds of Palestinians in administrative detention, but prime minister Benjamin Netanyahu's security cabinet approved using the measure for Israeli citizens after the arson attack in the West Bank on July 31.
Israel defends its use of detention without trial, saying it is needed to stem violence and allow for further investigation in cases where there is insufficient evidence to prosecute, or where going to court would risk exposing secret informants.
Mr Yaalon accused Ettinger and Slonim of "involvement in activity by an extremist Jewish group".
Meyer had been involved in "recent terrorist attacks as part of a Jewish terror group," Mr Yaalon said.
No specific incidents have been officially mentioned in relation to the arrests, although the crackdown was launched immediately following the torching of the Palestinian home.
Honenu, a group of Israeli lawyers representing the three detainees, condemned the use of detention without trial.
"Right now there are three detentions. In the coming days it could be 30, and we could end up with 300," one of the lawyers, Aaron Roze, told local media.
"These orders endanger the entire justice system."
Separately on Sunday, an Israeli police spokeswoman said the force's unit for combating ultra-nationalist crimes had carried out several arrests in Jewish settlements in the occupied West Bank.
She declined to give further details, citing a gag order.
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