Andrea Albutt wrote an open letter after recent violence at prisons in Hertfordshire and Wiltshire.
She said the unrest was causing "grave concern" - adding that governors faced "unacceptable stress and anxiety".
The Ministry of Justice (MoJ) said action had been taken to increase prison officer numbers.
But Ms Albutt said her members had seen "nothing tangible" from the MoJ to ease population pressures in prison, and the burden on staff.
She said recruitment remained in a "critical" condition, with a net increase of just 75 officers in the year 2016/17.
Training was "poor" and "unsuitable people" were being selected, she added.
The BBC's home affairs correspondent Danny Shaw said the Prison Governors Association had "traditionally been a voice of moderation".
"The criticisms are unlikely to be brushed aside," he said.
Data released last week from the MoJ showed a rise in violence in prisons, with 26,643 assaults in the year to March 2017 - 20% more than the previous year.
Of these, a record 7,159 were attacks on staff - equivalent to 20 every day.
Ms Albutt went on to describe the government's decision earlier this year, to separate operational control of the prison system from responsibility for policy, as "madness".
But an MoJ spokesman said the Her Majesty's Prison and Probation Service (HMPPS) - which replaced the National Offender Management Service - would "help to create a distinct, professionalised frontline service".
The spokesman added: "We know that our prisons have faced a number of long-standing challenges, which is why we have taken immediate action to boost prison officer numbers and have created Her Majesty's Prison and Probation Service.
"We need to create calm and ordered environments to help ensure effective rehabilitation, and we continue to work closely with the unions and all staff to help achieve these vital reforms and make prisons places of safety and reform."
In July, the union representing prison workers called for the resignation of prisons' boss Michael Spurr.
The general secretary of the Prison Officers Association, Steve Gillan, said his members had "lost patience" and accused the management of HMPPS of trying to "paper over the cracks".
This followed the revelation that Mr Spurr had received a bonus of up to £20,000 in 2016-17 on top of his annual salary of around £150,000.
The bonus was "awarded" in the previous year when the chief inspector of prisons said many jails were "unacceptably violent and dangerous".
The president of the Prison Governors Association has attacked the government's management of prisons in England and Wales.