Their deaths were sparked by rumours, spread mostly via Facebook, that children were being beheaded as offerings to fund what is set to be Bangladesh's biggest bridge, south of the capital. Dhaka.
Police chief Javed Patwary confirmed none of the victims were involved in child abduction.
"We have analysed every single case of these eight killings. Those who were killed by lynching mobs ... no one was a child kidnapper," he told reporters.
Twenty-five YouTube channels, 60 Facebook pages and 10 websites have been shut down amid concerns surrounding the dissemination of false information on social media.
Across the country, police have been ordered to monitor online platforms and issue public notices if misinformation is detected.
More than 30 people were reportedly attacked over the rumours, which have been circulating for around two weeks.
Eight people have been arrested over Ms Begum's murder, including a 19-year-old man, who is the prime suspect, according to local media.
He was allegedly seen beating Ms Bagum in a video that surfaced on social media.
Five people suspected to be involved spreading the rumours have been detained, according to AFP news agency.
Vigilante killings are not unusual in Bangladesh, but the latest mob lynchings have sparked concerns of growing lawlessness across the country.
According to data from human rights organisation Odhikar, 465 people were killed in extrajudicial killings in 2018, up from 155 in 2017.