Solo Sandeng, who had recently been promoted to organising secretary of the opposition United Democratic Party (UDP), died following his arrest and detention on Thursday by riot police, they said.
"We have received some reports that Solo Sandeng died in detention. We understand he died shortly after his arrest for participating in what we've been told by eyewitnesses was a peaceful protest," said Amnesty International west Africa researcher Sabrina Mahtani.
The circumstances of Sandeng's death were "as yet unknown", Mahtani said, calling on the authorities to conduct an immediate and thorough investigation and to release any other UDP members still being held.
Gambia's information minister did not immediately respond to a call for comment.
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Gambian security forces beat dozens of UDP activists who had gathered just outside the capital of Banjul on Thursday to press for reform, before rounding them up and taking them to an unknown location.
President Jammeh was out of the country when the protest happened, attending a summit of leaders from the world's Muslim countries in Istanbul.
A military officer and former wrestler, he has ruled the tiny west African country with an iron fist since he seized power in a coup in 1994, and is regularly accused of sanctioning a catalogue of human rights abuses.
Amnesty's Mahtani said further repressive measures against opposition activity was likely in the run-up to a presidential election in December widely expected to return Jammeh to power for a fifth term.