Steffi Graf, in New York preparing for the US Open that starts on 28 August, "is still under investigation, but the situation for her is unlike that of her father," said the Mannheim prosecutor, Peter Wechsung.
Wechsung explained that authorities had feared Graf's father, who has managed his daughter's career for 13 years, might try to flee the country or destroy evidence. Wechsung said there was no such fear regarding the 26-year-old champion.
Peter Graf had offered to post bail after his arrest on Wednesday, but a magistrate ordered him to be held in custody.
There was speculation that Steffi Graf might quit tennis because of her father's arrest and the pressures of an investigation.
Wechsung confirmed that Graf, 57, had been transferred to a prison hospital in Ludwigsburg after being examined by a doctor. The prosecutor said Graf Snr had some "physical complaints".
German media reported that Peter Graf had, over four years, a tax shortfall of at least DM10m (pounds 4.65m) on an estimated income of DM35m (pounds 16.2m).