Royal Mail said it had been forced to suspend deliveries to businesses on South Parade, Doncaster, during "adverse weather conditions".
It said the postman broke a shoulder after slipping on algae and moss on a pavement last Friday.
The council said there were no "defects" on the pavement.
Maxine Downes, from an accountancy firm on South Parade, said the suspended deliveries would cause "tremendous expense" and "so much inconvenience".
She added: "We rely on mail getting to us on time. This is going to be a delay for our customers.
"I've never noticed any moss or algae on the pavement and certainly I've never noticed it being slippery."
Morag Turnbull, from Royal Mail, said Doncaster Council had been notified of the "poor condition" of the pavement.
She said: "We have explained to customers in South Parade that we must, only during adverse wet weather conditions, suspend deliveries to their address as a precautionary measure until the pavement surfaces are improved by Doncaster Council.
"Customers will be able to collect their mail from Doncaster Delivery Office.
"We know this is inconvenient and we apologise to customers, but the safety and welfare of our staff is paramount and we only suspend deliveries if the safety of our postmen and women is at risk."
Gill Gillies, assistant director of environment for Doncaster Council, said: "Our highways officer has checked the full footway and there are no defects which require attention."