The man is reported to have died in hospital in Manaus after falling nearly 35 metres (115ft) when a cable broke.
The stadium is behind schedule and work is under way day and night to complete it by Fifa's end of year deadline.
It is the latest of several deaths during construction of Brazil's World Cup stadiums.
Two workers were killed in an accident on 27 November when a crane fell and destroyed parts of Sao Paulo's Arena Corinthians, which will host the opening game on 12 June.
Several more construction workers were hurt in the Sao Paulo accident, which delayed the stadium's completion date by several months.
The worker who died in the Amazon stadium - Arena Amazonas - was named as Marcleudo de Melo Ferreira, 22, by the company building the facility.
The firm said he was employed by a company subcontracted to construct the stadium's cover.
Brazil has admitted it is struggling to have all 12 venues completed on time.