Rita was found dead at her residence on Monday and police had initially ruled out any foul play, claiming that the death was due to an asthma attack.
But the locals, including Rita's brother, raised suspicion about her death.
The body, which was handed over to the family, was later taken back by police to conduct the postmortem which revealed a bullet in her chest, they said.
The couple had been living together for last six years in Anjuna village.
A case under section 302 (murder) of IPC has been registered against Fernandes, police added.