"It could be one to two billion euros," the minister told German radio, cautioning that a precise figure was "difficult to estimate."
Citing internal government projections, the Süddeutsche Zeitung daily earlier reported the costs would be €3 billion annually. "That order of magnitude seems a little high to me," countered Brüderle.
The minister's comments came as Chancellor Angela Merkel prepared to hold talks with heads of Germany's states to discuss future energy policy in the wake of Japan's nuclear crisis.
Merkel has said the disaster at the Fukushima plant in Japan was a turning point and announced a three-month moratorium on an earlier decision to extend the lifetime of Germany's 17 nuclear reactors.
Nuclear power is highly unpopular in Germany, and hundreds of thousands have taken to the streets to demand the reactors be switched off.
The economy and environment ministries have drawn up a joint plan for the accelerated development of alternative energy, which focuses notably on wind power.
"One thing is for sure, it's going to cost money," Brüderle said.