Nobody is responsible for her death, the woman wrote on Facebook
The reason for the murder is not yet clear.
Nabiganj police OC Liakat Hossain said they nabbed Refa Begum's husband Raihan Chowdhury on Saturday morning.
After primary questioning, he said Chowdhury strangled his wife late Friday night and then doused the body with kerosene before setting it on fire.
The body has been sent to Habiganj Sadar Hospital for a post-mortem examination.
The victim's family was preparing to file a case, OC Hossain said.