"No power in the world can prevent me from telling a man who I have known for many years and who I trust: I believe you," Schulz told dpa outside the prison in Curitiba in the south of the country.
The SPD has long maintained close contact with Lula's Workers' Party (PT), which is seeking to marshal international pressure to have Lula released by the time of the elections on October 7.
"This is a trip that I'm making for the SPD," said Schulz, who lost to Christian Democrat Chancellor Angela Merkel in the 2017 German elections.
"I encountered a very brave and fierce man today," Schulz, a former head of the EU parliament, said of the uphill battle facing Lula, whose party wants him to run in the election.
The SPD's current leader, Andrea Nahles, asked Schulz to undertake the mission, and the trip was also cleared with their SPD colleague, Foreign Minister Heiko Maas, Schulz asserted.
German diplomats were concerned that the visit, which could be seen as a signal of strong support from a well-known European visitor, might be interpreted as meddling in Brazilian domestic affairs.
Brazil is a deeply divided country, with violence increasing in Rio de Janeiro, the city that hosted the 2016 Olympics.
The Brazilian election is of "global significance," Schulz pointed out.
One poll indicates that just 13 per cent of people are content with democracy, following a series of corruption scandals.
Behind Lula in second place in pre-election polling is right-wing populist Jair Bolsonaro, who speaks highly of the military dictatorship that ran the country between 1964 and 1985 and has attacked black people and homosexuals in the past.
Lula's party registered him, as its candidate in the October elections earlier this month despite him having begun serving a 12-year prison sentence in April.
Lula was found guilty of corruption and money-laundering in connection with the renovation of a beachside penthouse, which was bankrolled by a company seeking contracts with the state oil giant Petrobras.
The PT regards the judicial proceedings as a manoeuvre by the political right to remove leftist Lula from the presidential race.
The electoral commission is expected to cancel Lula's candidacy on the grounds that the law does not allow people with criminal records to run for president. The court needs to announce its decision by September 17.
The PT might then replace Lula with its candidate for his vice president, former Sao Paulo mayor Fernando Haddad.
Haddad joined Schulz for Thursday's visit with Lula.
Lula rose from a shoe-shiner to one of the most popular politicians in Brazil's history. He is credited with pulling tens of millions of people out of poverty, partly through social programmes financed with oil money, during his 2003-10 presidency