The far-right EKRE party gained five cabinet positions after a strong electoral performance.
Party leader Mart Helme and his son both made alleged white power gestures at their swearing-in on Monday.
Marti Kuusik, minister of foreign trade and IT, resigned the next day over accusations of domestic violence.
The allegations against Mr Kuusik, an MP for the Conservative People's Party of Estonia (EKRE), began in media reports.
Police have since begun an investigation into the matter. He denies any wrongdoing, and regards the allegations as slander against him.
"In addition to a horrible media attack against me, the prosecutor's office decided to start a criminal investigation. In this situation I cannot work as a minister," he said in a statement.
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