The Bangalore Sessions Court granted anticipatory bail to Karthik, who is facing allegations of cheating and raping a model.
Meanwhile, the model, who claimed to be married to Karthik will reportedly challenge the bail granted to him.
On Thursday, an arrest warrant was issued against Karthik as he failed to appear before the court despite being served two summons.
Since the controversy erupted, Sadananda Gowda has overruled all allegations against his son, saying his son has been "falsely implicated" in the matter.
Karthik Gowda's whereabouts are unknown since the controversy erupted.
"Law will take its own course. I will not interfere in the matter. It is a personal matter. It is a falsely implicated complaint, as a minister I am here", Gowda had earlier told reporters when he was asked about the complaint filed against his son Karthik by the small-time Kannada model and actress.
A day after when Karthik got engaged at a ceremony at Kushalnagar in Kodagu District, a woman had claimed that she is married to him.
Karthik has been booked under Indian Penal Code (IPC) sections 376 (punishment for rape) and 420 (cheating).