The change will be in place from Monday, May 5, to allow for dry rot works to take place at the premises on Canal Street.
A date for when this maintenance will be completed is yet to be confirmed.
From next week, Renfrew residents will be able to pick up parcels at the Paisley Delivery Office on Underwood Road.
Councillor John Shaw says the lack of a return date to the original site is “concerning”.
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Writing on Facebook, he said: “I’ve had several local residents contact me regarding the Royal Mail notice, which has been shared online locally, confirming that the Renfrew Sorting Office will be moving to Paisley from May 5.
“The further information shared with the notice explained that this move is to allow dry rot works to be undertaken in the premises.
“Just to confirm, this is not something I had received any prior notice of. As a humble councillor, it’s not unusual that we don’t hear much from Royal Mail, though.
“The lack of an estimated return date is particularly concerning and I have written to the Public Affairs team at Royal Mail to seek clarity on when the works are expected to be complete and when the Renfrew Sorting Office will reopen.
“I will share any updates as soon as I receive a response.”
Some residents also voiced their “frustrations” on the move.
One said: “A difficult place to get to without transport!”
Another wrote: “Won’t hold my breath on them returning.”
Royal Mail have been contacted for comment.