Superintendent Bosco George told a news conference here that Rohit Monserratte, 21, "has been asked to immediately appear before the police for interrogation" but he was not found in either of his homes.
"The complaint was lodged by the mother stating that Rohit sexually assaulted her minor daughter, outraged her modesty and apparently raped her and sent text messages of an obscene nature via mobile phone," he said.
Meanwhile, Monserratte's father, Atanasio, was charged with abetting his son by allowing his mobile phone to be used to send the texts, George added.
The minister had assured the officer he would hand over his son as soon as possible, he added.
The unnamed German woman first complained to police in Calangute, about 10 kilometres (six miles) from the Goan state capital Panaji, on October 2, alleging that her daughter had been "mentally and sexually abused."
She also claimed that police in the former Portuguese colony wanted her to withdraw the complaint.
The case took a further twist Monday evening when the woman's lawyer, who is also an activist with a local social welfare charity, was attacked at a restaurant, police said.
Goa has come under the spotlight since February when a British teenager, Scarlett Keeling, was found dead on a beach. Police initially thought she had drowned but opened a murder probe under pressure from her mother.
Two local men are currently awaiting trial accused of plying the 15-year-old with drink and drugs, raping and leaving her for dead.