Widdecombe, 78, was found dead at her home in rural southwest England on Thursday with what police described as "serious injuries".
Officers arrested a 28-year-old white British man in Rotherham, northern England, late on Saturday.
Police urged the public not to speculate about possible motives while the investigation remains ongoing.
"At this point, there is still no information to suggest that this is a terrorism-related incident, and at this point, we are not looking for anyone else in connection with this murder," Chief Constable Matt Longman told reporters.
"Detectives remain open-minded about the potential motive. At this stage, there is nothing to suggest that it was politically motivated."
A second suspect arrested on Saturday was later released without charge.
A social conservative, Widdecombe served as a junior minister in John Major's Conservative government in the 1990s.
She stepped down from parliament in 2010 but later joined Nigel Farage's Reform UK as its immigration and justice spokesperson.
Widdecombe also found fame outside politics after starring in Strictly Come Dancing and Celebrity Big Brother.
Chief Const Longman said police were aware of online and public speculation, particularly with regards to a motive for Widdecombe's killing.
"Again, I urge people not to share or engage with that speculation – it's unhelpful, it doesn't aid our investigation, and particularly, it's distressing to the family and friends of Miss Widdecombe," he said.
Chief Constable James Vaughan said the force had mounted "an extraordinary response to a horrific murder of a very prominent public figure".
"The operation has been running at a lightning pace for 48 hours," he said.
"I am really pleased that we have a suspect firmly in custody and that will undergo some further work from us today.
"Well done to all – this is clearly British policing at its very best."
Widdecombe's personal driver of 10 years, Peter Horrell, lay flowers in front of her home on Saturday.
Horrell told reporters the politician "never mentioned any fear" for her safety and loved living in the village of Haytor.
Reform UK leader Nigel Farage also visited the village to pay tribute to Widdecombe on Saturday.
He told reporters the party has been going through its emails to check for patterns of abuse directed at Widdecombe, but has not been able to find anything.
Reform's MPs are now being given 24-hour security protection following her death, it has been reported.
ITV News has published a series of WhatsApp images which appear to show Widdecombe stopped responding to messages from a TV producer after the approximate time police believe the attack took place.
Two serving British members of parliament have been murdered in the last decade.
Labour MP Jo Cox was shot and stabbed by a Nazi-obsessed attacker during the Brexit campaign in 2016.
Conservative MP David Amess was stabbed to death in 2021 by a man inspired by the militant group Islamic State.
with PA
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