The editors of news agency IANS and Business Insider and the concerned reporters are mentioned in the FIR, though it does not identify them by name.
The reports carried by these organisations had suggested that the woman took the extreme step because she could not find food for the children due to the lockdown against coronavirus.
The authorities had, however, rejected this claim.
Cases have been registered under the Indian Penal Code, including section 505(1)(b), related to publishing or circulating a rumour or a report which may cause alarm or lead to an offence against the government.
Police have also invoked section 188 of the IPC (disobeying an order promulgated by a public servant).
Two others, Saleem Akhtar and Hansraj Meena, have also been booked, accused of circulating the report on social media.
The FIR has been registered at Gopiganj police station, Bhadohi Superintendent of Police Ram Badan Singh said.
District Magistrate Rajendra Prasad said the two media houses had reported that the woman, a daily-wage labourer, had nothing to eat and killed her five children by throwing them in the Ganga.
In reality, he said, the woman is not a daily-wage labourer and faced no shortage of food.
She took the extreme step after an altercation with her husband, the DM said.
The woman, Manju Yadav, has been arrested and charged with murder on the basis of a complaint by her husband Mridul Yadav.
The bodies of Aarti (12), Saraswati (10), Maateshwari (8) and Shivshankar (6), who were flung into the river on Saturday night, have been recovered. The fifth child is yet to be traced.
The couple quarrelled often, the SP said.
After throwing her children in the river, she sat at the ghat till the next morning and then told the villagers about it, police said. PTI CORR ABN NAV ASH