This incident comes just two days after several schools in Manchester and Cheshire were locked down over a series of "malicious communications", which are understood to have involved threatening staff and students.
Greater Manchester Police and Cheshire Constabulary said both forces were investigating the emails.
Cheshire Police stated that the email sent to schools in Cheshire Ellesmere Port had "made threats to pupils and staff."
Following this recent scare, the police launched a full investigation. Subsequently, they announced that they had arrested an individual in connection with an email sent to several schools in Leeds and Bradford.
The police have yet to disclose the specific nature of the threat.
However, a spokesperson for the West Yorkshire police commented: "Police are aware of an email which has been sent to several schools in Leeds and Bradford today."
"Police and officers are investigating the contents of the email and .are providing reassurance and safety advice to affected schools," they added.
According to the West Yorkshire police website, the contents of the email are being investigated whilst officers are providing reassurance and safety advice to affected schools.
The police website also mentioned that, contrary to some reports, the force has not issued any guidance to schools to enter a lockdown phase, and the force does not consider the threats credible.
One unidentified school told parents that the email had threatened "harm" to children and teachers across schools in Leeds, which prompted the school to keep all pupils locked indoors for the day.
According to Leeds Live, some of the schools understood to be affected by this threat so far include Sharp Lane Primary School, Richmond Hill Academy and Windmill Primary School.
Gildersome Primary School, another school affected by the startling incident, posted on their Facebook page yesterday afternoon to say that staff are being "extra vigilant" and "normal safeguarding procedures are being followed."
Additionally, several other schools in Leeds who did not receive an email have bolstered their security measures to reassure pupils, parents and caregivers.
One parent admitted to feeling "petrified" by the troubling news after she was alerted of the situation, also stating that it reminded her of the devastating incidents affecting various schools in the US, although none of the high-school shooters sent threatening emails first.
As a result of the threatening emails, authorities have now urged schools to be "extra vigilant" regarding site security and safeguarding, with a Bradford Council spokesperson commenting: "Police officers are providing reassurance and safety advice to affected schools."