Speaking at the start of a session of the Human Rights Council here, Bachelet said that the total death toll and harm done in Brazil, Bolivia and Paraguay in recent weeks "may never be known", Efe news reported.
Bachelet dedicated much of her speech, which opened three weeks of sessions, to the climate crisis.
Drawing on scientific evidence, she affirmed that the world had never seen such a big threat to human rights.
"This is not a situation where any country, any institution, any policy-maker can stand on the sidelines.
"The economies of all nations; the institutional, political, social and cultural fabric of every State; and the rights of all your people and future generations will be impacted," said Bachelet.
Regarding the Amazon, she urged authorities in Bolivia, Paraguay and Brazil to implement environmental policies and incentives in a bid to stave off any "future tragedies".
The human rights chief also denounced attacks on environmental activists "in virtually every region, particularly in Latin America".
"I am disheartened by this violence, and also by the verbal attacks on young activists such as Greta Thunberg and others, who galvanize support for prevention of the harm their generation may bear," she added.
Thunberg, the 16-year-old Swedish activist who kicked off the "Fridays for Future" movement in a bid to force world leaders to take action to protect the planet and who has been fronting youth protests outside the UN headquarters, has fallen victim to several verbal tirades on social media platforms.
Bachelet was opening the 42nd session of the UN Human Rights Council, an inter-governmental body comprised of 47 states that strives to fight for human rights.
The UN Human Rights chief's remarks came after seven South American countries have agreed measures to protect the Amazon river basin, amid concerns over fires in the world's largest tropical forest.
The Amazon is a vital carbon store that slows down the pace of global warming, and 60 per cent of it is located in Brazil. So far this year, more than 80,000 fires have broken out in rainforest.
( With inputs from IANS )