Nurjahan Begum, who lived alone, was found dead in her tin-roofed house near the Martyrs' Graveyard in the capital's Mirpur last evening, police officer Farukul Islam said.
"Her throat was slit," the Daily Star newspaper quoted Islam as saying.
The body was sent to Dhaka Medical College morgue for an autopsy.
Citing locals, the paper said Nurjahan was known as Kheta Pagli and she had quite a following for the last eight years. Her followers considered her a "pir" or Sufi mystic. They built her the house and many of them gave her food and money.
There have been systematic assaults in Bangladesh in recent years specially targeting minorities, secular bloggers, intellectuals and foreigners.
Over a dozen Sufi Muslims have been found with their throats slit in Bangladesh since 2013. The authorities blamed homegrown Islamist extremists for the killings.
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