The man, who has been identified by media as Christian Brückner, had been serving a seven-year sentence that stemmed from his 2019 conviction for the rape of a 72-year-old American woman in Portugal.
He left the prison at Sehnde, near Hannover in northern Germany, on Wednesday.
In June 2020, German prosecutors said the man was being investigated on suspicion of murder in connection with McCann's disappearance on May 3, 2007, from an apartment complex in the Portuguese resort of Praia da Luz. They said they assumed the girl was dead.
Police have since carried out more searches in Portugal but Brückner, who has denied any involvement in her disappearance, has not been charged in the case.
The investigation is not affected by his release. Brückner also remains a suspect in an investigation into McCann's disappearance being conducted by Britain's Metropolitan Police, who say he refused their request for an interview.
His lawyer, Friedrich Fülscher, has said charges would have been filed against his client long ago if there had been sufficient evidence.
The 48-year-old spent many years in Portugal, including in the Algarve resort of Praia da Luz around the time of Madeleine's disappearance.
Investigators in the UK, Portugal and Germany are still piecing together what happened on the night three-year-old Madeleine disappeared. She was in the same room as her brother and sister - two-year-old twins - while their parents, Kate and Gerry, had dinner with friends at a nearby restaurant.
The suspect was tried last year over several unrelated sexual offences he was alleged to have committed in Portugal between 2000 and 2017 and was acquitted in October. The presiding judge said the evidence was insufficient for a conviction.
Brückner still faces an October 27 court date in Oldenburg in northwestern Germany in a case in which he is accused of insulting a prison employee. A court sentenced him to six weeks in prison for that, but the defence has appealed.
