The 55-year-old suffered lower back, chest and shoulder wounds during the attack at Haymarket about 9.20am on Friday.
He was treated by NSW Ambulance paramedics and transported to hospital in a critical but stable condition.
A 37-year-old man was arrested and taken to a police station Darling Harbour.
Footage shared to social media on Friday showed a heavy police presence outside the Service NSW building in the inner city.
The building will be closed for the weekend, the customer service department said.
"The welfare of our staff is our highest priority. Every possible support will be made available for this staff member and his family.
"All other staff at the centre are being offered counselling and support."
Opposition Leader Mark Speakman said he was shocked by the stabbing attack on a frontline worker.
"Nobody deserves to be harmed while doing their job serving the public," he tweeted on Friday afternoon.
"Thank you to the first responders who provided assistance. Wishing for a quick recovery."
Detective Superintendent Martin Fileman and Customer Service department secretary Emma Hogan will address media later on Friday.
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