The two redundancies are part of a restructure after Linehan started at the Sydney charity in June.
"Particularly given recent history, it's really important that as an organisation we are financially very disciplined," he told AAP.
Carriageworks, which hosts commercial events such as Australian Fashion Week and art show Sydney Contemporary, went into voluntary administration in 2020 during the COVID-19 pandemic, before being rescued by philanthropists.
The restructure was a "difficult decision" that came out of a five-month review, Linehan said in a staff email seen by AAP.
Carriageworks was facing "some real challenges", he said in the email.
"In particular, we've had to look long and hard at our financial position and find a workable business model."
One of the jobs cut is that of the manager responsible for installing exhibitions, and the other is a curator who works with The Clothing Store artist residencies as part of their brief.
The Clothing Store program has supported more than 30 artists since it was established in 2017, including well known figures such as Tony Albert and Thea Anamara Perkins.
Other artists AAP spoke to were concerned about the future of the residency program.
An expression of interest process for residencies in 2024 closed last Monday, and Linehan confirmed the program would continue with next year's selection process currently under way.
Carriageworks had about 35-40 workers, including other staff able to work on exhibitions, Linehan said.
Linehan has previously led the Sydney Festival and Vivid Live at the Sydney Opera House, as well as roles overseas.
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