His side are ahead of England in their qualifying group for Euro 2008.
Russia lie second in group E, behind leaders Croatia but a point ahead of England.
Hiddink, who can appeal against the decision, has always denied defrauding the tax authorities.
Hiddink, the former South Korea, PSV Eindhoven and Australia boss, had been tipped to succeed Sven-Goran Eriksson as England boss after the 2006 World Cup.
His close relationship with Chelsea owner Roman Abramovich also led to rumours he was set to replace Jose Mourinho as manager at Stamford Bridge this summer - but Hiddink has dismissed the reports.