Police will allege Carlino killed Kumar some time after 9pm on Wednesday night, wrapped her in plastic and tape, and left her body in bushland, The Daily Telegraph reported.
He was refused bail to appear before Parramatta Bail Court on Sunday.
The woman had been reported missing to police on Thursday morning after her family raised the alarm.
Carlino said she had left the house in her pyjamas and her not taken her phone with her.
"I've told police all of the places I think she could be," he said.
Carlino and Kumar, who are understood to have been living together at the time of her disappearance, took over the franchises of the popular Hornsby Mad Dogs & Englishmen pet walking service in October last year.
The Sydney mum, who was also a part-time model, had been featured in a variety of magazines, including French fashion publication Malvie and Amsterdam-based Selin Magazine.
Her disappearance sparked co-ordinated police searches of surrounding areas over the last three days, with assistance from the police air wing and dog unit.
About 5.50pm on Saturday, police located the body of a woman during the search in bushland off Laurie Rd, Dural.
A crime scene was established, which is being examined by specialist forensic police.
Police said investigations are continuing.
Anyone in Australia with information about this incident is urged to contact Crime Stoppers: 1800 333 000.
