The sudden resignation of the minister is likely to deepen the turmoil around Brazil's flailing response to the pandemic, in what is one of the world's worst hotspots.
Teich, whom the far-right president, Jair Bolsonaro, had criticized as being too timid in the push to reopen the economy and advocate the use of anti-malarial drugs to fight the virus, submitted his resignation via Whatsapp on Friday morning. Later in a press conference, he did not explain the reasons for his resignation.
"Life is made of choices, and today I chose to leave. I did the best I could in this period. It is not simple to be at the head of such a ministry at such a difficult time. I want to thank my team that has always worked intensively for this country," Teich said in a brief speech.
Teich was Brazil's second health minister to leave office in less than a month.
His predecessor, Luiz Mandetta, was fired by Bolsonaro on April 16 following disagreements over social isolation measures, which Bolsonaro has dismissed as unnecessary.
Teich's resignation has caused dismay among doctors fighting the pandemic. Albert Ko, a professor of epidemiology at the Yale School of Medicine, blamed "the lack of leadership and poor governance."
"To lose two health ministers will really have a dramatic impact on the country's ability to contest the epidemic," said Ko, who has extensive experience working in Brazil.
On taking office, Teich initially appeared to follow Bolsonaro's line, arguing that bolstering Brazil's economy was as important as controlling the pandemic's growing death toll.
But in recent weeks, Teich had increasingly disagreed with Bolsonaro's insistence in broader use of hydroxychloroquine as a treatment for the COVID-19, which the minister has resisted due to a lack of scientific evidence.
Teich's resignation comes a day after Brazil reported a record number of new COVID-19 cases in the country, totaling 13,933 deaths from the virus.
Meanwhile, the surprise resignation spurred criticism of the right-wing president from politicians and calls for his impeachment. In Rio de Janeiro and Sao Paulo, where the disease has pushed public hospitals to capacity, Brazilians banged pot and pans from their windows in protest.