The probe into the death of David Amess, 69, will be led by the Counter Terrorism Command of the Metropolitan Police, the agency Friday.
Amess was speaking at a Methodist Church in Essex when a man entered and stabbed him, authorities said. Police arrived after 12:05 p.m. local time and arrested a man for the stabbing.
Amess was stabbed multiple times and died at the scene. The suspect, an unidentified 25-year-old man, is being held in police custody in Essex.
"It is believed that he acted alone, and we are not seeking anyone else in connection with the incident at this time," police said.
Investigators were conducting searches at two addresses in the London area in connection with the murder, police said.
Amess was part of Prime Minister Boris Johnson's ruling Conservative Party. He had been a member of parliament since 1983 and a member of his current constituency – Southend West in Essex – since 1997.
In a tweet, Johnson called Amess one of the "kindest, nicest, most gentle people in politics."
"David was a man who believed passionately in this country and in its future," Johnson said in a video accompanying the tweet. "We've lost today a fine public servant and a much-loved friend and colleague."
The slaying came five years after another member of British Parliament, or MP, Jo Cox, was killed by a man with white supremacist views. Cox, 41, a member of the Labour Party, was shot and stabbed in June 2016 outside a library where she was slated to meet with her constituency.