The decision by Judge Humberto Otazu, which was seen by Reuters, will be appealed, Leoz's lawyer said.
Leoz, 89, who has been under house arrest since mid-2015, is being investigated by the U.S. Justice Department along with other leaders and executives accused of accepting bribes for broadcast rights and marketing.
Leoz's lawyer, Ricardo Preda, told journalists he would appeal the decision. Preda said he had not been notified by the court and argued his client should not be extradited because private bribery is not a punishable crime in Paraguay.
Otazu said in an official document that a medical board, including a forensic officer of the judiciary and a doctor proposed by the defence, should report on Leoz's health status before his extradition.
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Paraguay received the formal request for Leoz's extradition in July 2015. According to Paraguayan laws, the former sports leader's age is not a barrier to extradition.
Leoz was in charge of Conmebol for 27 years until he resigned in 2013, blaming health reasons in the midst of an investigation by the FIFA ethics committee. He also was a member of the FIFA executive committee for more than a decade.
Otazu's decision comes as the trial begins in New York for Juan Angel Napout, Leoz's successor as president of Conmebol, the former president of the Peruvian federation Manual Borga and former head of the Confederation of Brazilian Football Jose Maria Marin.
(Reporting by Daniela Desantis; Writing by Cassandra Garrison; Editing by Bill Trott)
