Independent Education Union of Australia NSW/ACT Branch Secretary Mark Northam says teachers will walk off the job on May 27.
"Taking protected industrial action is no small thing - we don't take it lightly," he said on Thursday.
"Teachers and support staff across both the government and non-government sectors are dedicated professionals pushed to breaking point.
"Schools have been running on good will, but it is rapidly evaporating."
The industrial action follows a 24-hour strike on May 4 by thousands of NSW public school teachers concerned about a chronic teacher shortage.
They are demanding a pay increase above the 2.5 per cent cap on NSW public sector wage rises.
IEU members participated in a formal balloting process with all 11 Catholic dioceses endorsing the strike.
"The sharply rising cost of living, lack of real wages growth, ever-increasing workloads and the pandemic have caused crippling staff shortages in Catholic schools - our members are exhausted and burnt out," Mr Northam said.
Catholic school employers had followed the NSW government's lead in limiting pay rises to 2.04 per cent - "a short-sighted approach that has resulted in the current staffing crisis", he said.
"Teachers are leaving the profession and graduates are not entering it."
The IEU wants a pay increase of 10-15 per cent over two years, pay parity with colleagues in public schools, less paperwork and more class preparation time.
Meanwhile, new data from the NSW Secondary Principals Council has revealed nearly a quarter of principals are set to retire over the next three years.
NSW Labor leader Chris Minns says the survey makes sober reading.
"Unfortunately it is not a surprise that teachers and principals are looking to leave the profession while the government fails to fix ongoing staff shortages and workload issues," he said.