Three people were beaten to death in Seraikela district on Thursday morning and three more were killed in Jamshedpur district in the evening.
A senior police official told BBC Hindi that the incidents happened because of "rumours that a child-kidnapping group was active in these areas".
Police have not yet arrested any suspects in the two cases.
It is not clear when and how the rumours started. But RK Malik, a spokesperson for the state police, said people had become increasingly worried by them.
"They are suspecting anybody unknown to them [to be] a child kidnapper," he said.
He added that police officers had been injured while trying to stop the mob in Seraikela.
The state's top policeman, DK Pandey, said police had not received any reports about kidnapped children in these two districts in recent days. "So these are just rumours," he said.
More than 100 police officials had been deployed in each district to provide security and quell rumours, he added.
Jharkhand is one of India's poorest states.
India has seen sporadic incidents of mob justice and vigilantism in the past. In April, a man transporting cattle died after being beaten by a mob.
A Muslim man in northern India was also beaten to death in 2015 over rumoursthat his family had slaughtered a cow - considered sacred by Hindus.
In the north-eastern state of Assam, more than 70 people - mostly women - were beaten or stoned to death between 2010 and 2016 on suspicion of practising witchcraft, and in 2015 a suspected rapist was taken by a mob from a prison in Nagaland and killed.