Modi, who is seeking a rare third consecutive term, referred to Muslims as "infiltrators" during a campaign speech on Sunday, drawing widespread criticism from opposition groups
Chief executives (UNO) of Haluaghat and Gouripur Upazilas announced the results on Monday night.
The Mymensingh-1 constituency fell vacant after the death of state minister for social welfare Promode Mankin on May 11.
His son Jewel Areng has won the seat in the by-election by bagging 170,204 votes with Awami League’s boat symbol.
His closest contestant independent candidate Selina Khatun got 14,338 votes.
Former state minister for health Mujibur Rahman Fakir, who represented Mymensingh-3 constituency, died of cardiac arrest on May 2.
Awami League candidate Nazim Uddin Ahmed has won the seat by polling 119,438 voters.
Jatiya Party candidate Shamsuzzaman Zaman got 4,372 votes.