The deceased has been identified as Dr Kiran Honannavar, an anesthesiologist at Chirayu Hospital.
His wife, Dr Priyanka, an ophthalmologist, has been taken into custody for questioning. Their injured son is undergoing treatment at a private hospital.
Family's concern led to discovery
According to Hubballi-Dharwad Police Commissioner N Shashikumar, the case came to light after Dr Kiran's relatives repeatedly tried to contact him.
"They were initially told by his wife that he was resting and later that he had gone out. When he remained unreachable until evening, family members went to the apartment and found him lying in a pool of blood," the commissioner told the media.
The relatives also found the injured child inside the house and alerted police.
Police: No signs of outsider entry
Investigators said preliminary findings suggest that no outsider is believed to have entered the apartment.
"This is a highly secured residential complex. At the time of the incident, only three people - the husband, wife and child - are believed to have been inside the house," Commissioner Shashikumar said.
Police added that the husband was found dead in one room, while the child was discovered injured in another. The exact sequence of events has not yet been established.
Wife in shock, giving inconsistent statements
Officials said Dr Priyanka is currently in a state of shock and has been making what investigators described as inconsistent and unusual statements.
"We are verifying her version of events and gathering information from both families to determine the motive behind the incident," the commissioner said.
Police said there was no indication of any dispute with neighbours.
CCTV footage, post-mortem under examination
Authorities have registered a case at the Suburban Police Station. CCTV footage from the apartment complex will be examined as part of the investigation.
Police said the precise cause and circumstances of the murder will become clearer after the post-mortem examination and further forensic analysis.
While some relatives have alleged that Dr Priyanka was responsible for the killing, police have not confirmed her involvement and stressed that the investigation remains ongoing.
"At this stage, we are exploring all angles. The incident appears to have stemmed from a domestic dispute, but the exact motive is yet to be established," a police official said.
Officials also said they have not officially confirmed reports regarding the child's alleged mental health condition, and that aspect is also being verified.