Ali Harbi Ali is the son of an ex-media adviser to a former prime minister of Somalia.
Amess, 69, from Prime Minister Boris Johnson's Conservative Party, was knifed repeatedly as he met constituency voters in a church on Friday in Leigh-on-Sea, east of London.
Police said they had arrested a 25-year-old British man at the scene on suspicion of murder and have said it is believed he acted alone. They have not named the suspect but used additional powers under anti-terrorism laws to detain him until Oct. 22.
A British source close to the investigation named Ali Harbi Ali, a British citizen, as the detained suspect.