Widdecombe, 78, was found dead at her home in rural southwest England on Thursday with what police described as "serious injuries".
Officers arrested a white British man in Rotherham, northern England, late on Saturday.
"Following new information and evidence, they (counter-terrorism police) are now leading on the investigation into the horrific murder of Ann Widdecombe," interior minister Shabana Mahmood posted on social media platform X on Monday.
"The police are pursuing multiple lines of enquiry to establish the motivation for this attack," she said, adding that she would update MPs in parliament later in the day.
The Devon and Cornwall police force, who were previously investigating the suspected murder, had said on Sunday that there was no evidence suggesting there was a political motive or that the incident was terrorism related.
Widdecombe was first elected a Conservative MP in Kent in 1987, went on to serve as a member of the European parliament for the Brexit Party and then a spokeswoman for Reform UK.
She also found fame outside politics after starring in Strictly Come Dancing and Celebrity Big Brother.
- with PA
6°C