Parvin Akter, hailing from Gazipur's South Panishail locality, is a councillor for ward number 1, 2, and 3.
Her husband Minhaz Uddin filed a complaint with Joydebpur police on Friday night.
Joydebpur Police Station's Sub-Inspector Md Didar said Councillor Parvin went out at around 8am to attend an arbitration at a nearby village.
Her husband lodged a police complaint at around 10pm, as she did not return home.
Parvin's brother Md Rafiq Mia said she left her mobile phone at home as it did not have enough charge.
"We looked for her at our relatives and places she could have possible gone to, but the search is so far futile, he said.