Police discovered the crime after the man was evicted from his rented accommodation in Kicukiro, a suburb of the capital, Kigali.
They were called after the suspect had defaulted on rent payments for months.
A police officer told local media the victims appeared to have been sex workers. They included men and women.
BBC The man had reportedly failed to pay rent
Murder is relatively uncommon in Rwanda and this case has shocked the country.
An unnamed police official told Rwanda’s private newspaper The New Times that the man had put up a fight when officers went to evict him on Monday.
“He apologised and cried excessively, which raised our suspicions. It is at the police station where he confessed to having killed some people, prompting Rib [Rwanda Investigation Bureau] to investigate,” the official said.
A number of bodies have been recovered but the exact number would be determined after forensic investigations, said Rib spokesman Thierry Murangira.
“He operated by luring his victims, mostly prostitutes, to his home where he would rob them of their phones and belongings and then strangled them to death and buried them in a hole dug in the kitchen of his rented house,” Mr Murangira said.
He is yet to be formally charged.
The man had reportedly been arrested in July for allegedly robbing, raping and threatening some women, but released as there was insufficient evidence.
