The decision will affect nearly 200 people living in its facilities at Sylvania in the south, Carlingford in the northwest, as well as its Narrabeen home on the northern beaches.
The decision comes after the closure of its Wesley Tebbutt facility at Dundas in northwest Sydney last year.
CEO and superintendent Reverend Stu Cameron said several factors were behind "the difficult decision", including "challenges to workforce and flow-on impacts from the national reforms to aged care".
The aged care royal commission made 148 wide-ranging recommendations, and the federal government has committed to having registered nurses in aged care homes around the clock from July.
The sector is experiencing chronic staff shortages, but the minimum pay rate is due to increase by 15 per cent from July.
"Wesley Mission supports these once-in-a-generation reforms, improving quality for all care users," Rev Cameron said on Thursday.
"But we took the extraordinarily difficult decision it was time for us to exit the sector.
"There's all sorts of pressures, workforce pressures, cost pressures."
He said Wesley's aged care offering was small compared with the diverse range of community services it provided around NSW.
"It is ... a challenging environment to be a smaller provider," Rev Cameron said.
MyCarePath has been appointed to help the 199 residents find a new home before centres close at the end of May.
"We're committed to remaining open until every one of those residents finds a suitable, appropriate new home and care service," Rev Cameron said.
He said the 249 workers affected would be helped to find a new role within the organisation or with a different provider.
"Wesley Mission's support for older people in NSW continues, focusing on providing in-home care and retirement living to help people stay in their homes for longer," Rev Cameron said.
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