Singh confessed to killing Bibi during an interview around midnight Wednesday, police said.
Officers believe Singh was angry over what he perceived to be disrespectful behavior by Bibi when he armed himself with a hammer and confronted her on Tuesday.
Police told KCRA that there were "some previous issues" between Bibi and Singh regarding her acceptance into the family.
Neighbor Vanessa Sanchez told the news station that she called 911 after learning about the death from Bibi's husband.
"I was going to the gym, and he was like, 'Oh, what could I do? My wife is dead,'" she said.
Amarjit has no prior criminal record, according to KCRA. Authorities charged him with murder and booked him into Solano County Jail.