Abdolsamad Khoramshahi said Shahla Jahed, 40, was hanged at 0500 local time (0130 GMT) at Tehran's Evin prison, the official Irna news agency reported.
International human rights groups have campaigned for her release since she was jailed more than eight years ago.
The execution is the 146th in Iran this year, according to AFP news agency.
On Tuesday, Amnesty International made a last-minute appeal for the sentence to be halted, saying Jahed had not received a fair trial.
Jahed, who had been living with footballer Nasser Mohammadkhani in Tehran under a temporary marriage, was found guilty of stabbing to death his first wife, Laleh Saharkhizan, in 2002.
She first confessed to the murder, but then retracted the statement in court.
According to the Irna news agency, Jahed prayed prior to the hanging and then burst into tears and shouted for her life to be spared.
Mr Mohammadkhani, a top Iranian footballer in the late 1980s who later became coach for Tehran's Persepolis club, was present at the execution, reports said.
Shahla Jahed Has Been Hanged
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