Widdecombe, 78, was found dead at her home in rural southwest England last Thursday with what police described as "serious injuries".
She was a prominent member of Nigel Farage's populist Reform UK, having left the Conservatives after she stood down from parliament in 2010.
Police said they arrested a "white British" man in Rotherham, northern England, late on Saturday on suspicion of her murder, and initially said there was nothing to suggest a terrorism link.
"On Wednesday Ann Widdecombe was murdered in her home. The circumstances of her death are extremely distressing. Counter Terror Policing have now taken the lead in the investigation," Mahmood told MPs.
Mahmood said that "new information" had come to light which had changed the character of the investigation but added that the suspect was not known to the United Kingdom's counter-radicalisation scheme Prevent.
Counter-terrorism police said that the suspect had been rearrested on suspicion of commission, preparation or instigation of acts of terrorism, and appealed to the public for information about the case.
"We are pursuing multiple lines of enquiry to establish the motivation for this attack," said Laurence Taylor, head of National Counter-Terrorism Policing.
"Our priority is progressing this investigation quickly."
Security for politicians is under scrutiny as two serving UK 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.
Saying that Cox and Amess were also on her mind, Mahmood said that Widdecombe's death "raises questions about the security of those in public life," adding that government would work with parliament on how to protect MPs and others involved in politics.
"I recognise the particular concern that the Reform Party will feel today, and of course Nigel Farage, the party's leader," Mahmood said, offering him a meeting to discuss security.
Widdecombe was known for her socially conservative views, first as a junior minister in Conservative prime minister John Major's 1992 to 1997 government and latterly as an immigration and justice spokeswoman for Reform UK.
She also found fame outside politics after starring in the TV shows Strictly Come Dancing and Celebrity Big Brother.
Tributes have poured in following her death from across the political spectrum.
with PA
