Serra, 74, said health problems made him unable to keep up with the rhythm of leading the foreign ministry of Latin America's biggest nation.
He did not disclose what medical problems he is addressing. A government source said it was related to his spine on which he has had surgery in the past.
Serra was a highly experienced official and former presidential candidate.
Temer has low popularity ratings amid a vast corruption scandal. He took over as president in May to replace Dilma Rousseff, who was later impeached.
Temer already had lost seven leading members of his government -- six ministers and a senior adviser.
Brazil's economy shrank 3.5 percent in 2015 and an estimated 3.6 percent last year.
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