The polling is being held for one seat of Khyber Pakhtunkhwa Assembly, PF-42 Hangu-1.
The threat by the Tehreek-i-Taliban Pakistan (TTP) was conveyed through leaflets found by people in Hangu bazaar yesterday, the Dawn reported.
Police confirmed the TTP had issued the threat, it said.
The Taliban had issued a similar warning during the May 11 general elections and had taken away ballot boxes in some parts of Hangu.
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DIG Ishtiaq Marwat said that out of 89 polling stations in Hangu, 51 have been declared very sensitive and personnel of police, Frontier Constabulary and army had been deployed there.
Fool-proof arrangements had been made for the by-polls, he added.
Voting for 41 National and Constituent Assembly constituencies began today.