Mr Toledo, who governed from 2001 to 2006, is accused of receiving the graft money from Brazilian construction firm Odebrecht in return for awarding public works contracts.
He is not in Peru - he lives in the US and is currently in Paris.
In recent media interviews he has denied any wrongdoing.
Judge Richard Concepcion ruled that Mr Toledo should be remanded in custody at the earliest opportunity, rejecting a request for bail from the former president's lawyers.
Odebrecht is at the centre of a multi-national corruption scandal. It admitted as part of a plea deal with the US justice department to paying nearly $800m (Â£640m) in bribes to governments across Latin America.
They admitted paying $29m in Peru to secure contracts between 2005 and 2014.
That time spans the presidencies of Mr Toledo and his two successors in office, Alan Garcia and Ollanta Humala. His successors have also denied any wrongdoing.
Peruvian media reported that Odebrecht's former executive director in Peru, Jorge Barata, accused Mr Toledo of receiving $20m in bribes in exchange for granting the firm a contract to build stretches of a highway linking Peru and Brazil.
Mr Barata is co-operating with prosecutors in his native Brazil and Peru as part of a plea bargain.
Mr Toledo has strongly rejected the allegations, saying: "Let Mr Barata say when, how, where and to which bank he sent me $20m. I won't stand for this!"
Investigators searched Mr Toledo's home for five hours on Saturday. The attorney general's office said documents found at the home would now be evaluated.
Mr Toledo was in France at the time of the search and said he was "outraged by this political lynching coming from my traditional enemies".
The current president of Peru, Pedro Pablo Kuczynski, has urged Mr Toledo to return to Peru to face questioning.
A Peruvian judge has ordered the arrest of the country's former president Alejandro Toledo over allegations that he took $20m (Â£16m) in bribes.