One poll suggests 52.3% voted against the proposal to amend the constitution, while another suggests it was 51%.
The change would have let Mr Morales, who says he needs more time for reforms, remain in power until 2025.
Opposition supporters have been celebrating the referendum result in parts of the main city, La Paz.
Mr Morales, an indigenous Aymara and former coca leaf producer, took office in January 2006.
The president's current term ends in 2020.
He is still a popular leader, in part because he is Bolivia's first head of state of indigenous origin, and the economy has grown steadily over the past decade, the BBC's Americas Editor, Leonardo Rocha, reports.
But many thought Evo Morales should not be allowed to serve 19 consecutive years as president, our editor adds.
(BBC News)