Fresh from a spat with French President Emmanuel Macron over his management of wildfires raging in the Amazon, Bolsonaro said Bachelet was interfering in Brazil's internal affairs by "attacking our courageous civil police and military."
The leftist former Chile president was "following Macron's line," Bolsonaro tweeted, later taunting Bachelet by praising Augusto Pinochet's 1970s dictatorship in Chile, under which both she and her father were tortured.
Bachelet had told a news conference in Geneva that her office was concerned by a hike in killings by police officers and by broader human rights restrictions in Brazil.
She said that in Rio and Sao Paulo alone, "1,291 individuals were killed by the police. It might be police action, but what I want to highlight is there is an increase from 12 to 17 percent compared to the same period last year."
"In recent months, we have seen also a shrinking of civic and democratic space, highlighted by documented attacks against human rights defenders, restrictions on the work of civil society and attacks on educational institutions," Bachelet said.
Bolsonaro's harshest words for Bachelet came later, in comments to reporters outside his Brasilia residence.
Bachelet "is saying that Brazil is losing democratic space, but forgets that her country would be a new Cuba if it wasn't for those who had the courage curb the left, including her father -- a communist brigadier general -- in 1973."
Alberto Bachelet, an air force general, was arrested and tortured after a coup brought right-wing dictator Augusto Pinochet to power. Bachelet died in jail in 1974.
"When you have people with nothing to do, they occupy the UN human rights chair," he added.
The row comes just weeks away from the UN General Assembly in New York, which Bolsonaro said he would attend "in a wheelchair or a stretcher" if necessary to defend his policy on the Amazon, despite facing surgery next Sunday.
The former army captain recently accused Macron of meddling in Brazil's affairs after the French president called for the internationalization of efforts to protect the Amazon after Brazil failed to control raging wildfires and deforestation.
Brazil's president further accused France and Germany of "buying" Brazil's sovereignty after the G7 group of rich democracies offered $20 million in Amazon fire aid.
He initially rejected the money unless Macron withdrew "insults" made against him.
In her news conference, Bachelet said that since 2012, "Brazil has been one of the five countries in the world with the highest number of killings of human rights defenders."
- 'Environmental psychosis' -
=============================
"From January to June this year at least eight human rights defenders were killed," she said.
She said her office had documented killings over land disputes, but also in violence between environmental activists and illegal loggers, miners and farmers.
Since taking office in January, Bolsonaro has been accused of harming the Amazon and indigenous tribes in order to benefit his supporters in those industries.
"We are experiencing a real environmental psychosis," Bolsonaro said recently.
He has attacked environmental agencies and pledged to crack down on what he has called radical activism, and also questioned the latest official figures showing deforestation increasing by 88 percent in June compared with the same period last year.
On the eve of the G7 summit in France in August, Macron declared the forest fires, which are also affecting Bolivia, an "international crisis" and put them on the agenda of the gathering.
Macron also accused Bolsonaro of lying to him about Brazil's climate change stance.
Bolsonaro reacted furiously, accusing Macron of having a "colonialist mentality."
The Brazilian leader later said he will stop using disposable pens made by France's Bic.
Under growing pressure to do more, Bolsonaro issued a nationwide 60-day ban on burning vegetation in the vast Amazon basin.