Reports said the footballer had initially looked to fly from Turin, where he is in pre-season training, to Argentina on hearing the news of the kidnapping but he remained in Italy.
Tevez said on Twitter that his father had been released without harm.
"I thank everyone for their support always. I'm able to tell you my father is ok, safe and sound. That's what's most important," he said on his Twitter account (@carlitos3210).
"I also thank... the Buenos Aires and Federal and Anti-kidnapping police (forces) for their support for my family."
The amount paid for Segundo Tevez's release was not revealed but media reports said it was 400,000 Argentine pesos ($48,900).
Tevez's brother Diego told local radio station La Red that at first his father only had his vehicle stolen and was immediately released, but they went back for him when they saw his name on its registration.
"When they realised he was the father (of Carlos Tevez) because of the 'green card' they went back for him and asked for the ransom," Diego Tevez said.
The daily La Nacion, quoting sources close to the police operation, reported that the kidnappers had told Tevez's father: "We admire your son, but we have to do this to work."
Despite being in brilliant form in Serie A for Juventus last season, Tevez was not chosen by Argentina coach Alejandro Sabella for the World Cup finals in Brazil.
Argentina lost 1-0 to Germany in the Rio de Janeiro final two weeks ago.
"We're annoyed with Sabella because he didn't call him up to the national team," La Nacion also quoted the kidnappers as saying.