The three were taken to hospital after being attacked in the early hours of Saturday morning.
They were also verbally abused, police said.
John Walsh, the council chief executive, said: “This was an unwarranted attack on three council workers, simply out doing their job and delivering key services for our city.
“I condemn it completely and urge anyone with any information to help police with their enquiries.”
Police have appealed for information on the incident.
Inspector Knowles said: “We received a number of reports at around 12.40am that three men, believed to be council workers, had been attacked by two unknown males while carrying out their duties in the Little Donegall Street area.
“Officers spoke with all three of the injured men, who had been punched to the face and neck, with one of the men also sustaining an injury to his hand.
“It was reported that an unknown male had approached the council workers and began being verbally abusive towards them, before physically assaulting them. He was then joined by a second, unknown male, who also physically assaulted the men.
“One of the suspects was described as being of slim build with blond hair and was wearing a grey tracksuit.
“All three injured men subsequently attended the hospital for treatment to their injuries.
“Our council workers are a vital part of our community and assaults on them whilst doing their job will not be tolerated. I would urge anyone who may have been in the area and witnessed this to come forward and assist us with our enquiries, which are ongoing.”
DUP MLA Phillip Brett said it was a “disgraceful attack” on staff who were simply going about their jobs serving the public.
“I have spoken directly with the police about this incident. Those responsible must be identified and held fully accountable,” he added.
“It is also vital that any motivation behind this attack is published.
“Council staff deserve transparency, reassurance and the right to work without fear or intimidation.
“There can be absolutely no justification for targeting public sector workers. I stand firmly with the staff affected and their colleagues.”
Alliance councillor Michael Long said it was an “utterly shocking incident”.
“My thoughts are with the victims who were attacked, who were simply out doing their jobs, and I wish them a full recovery,” he said.
“Those responsible must face the full consequences of their actions, and I would urge anyone with any information to contact the police to assist with their investigations.”
Sinn Féin councillor Ronan McLaughlin also condemned the attack.
He said: “This was a shocking assault on these workers simply carrying out their jobs on behalf of the people of our city.
“I condemn those involved and want to express my thoughts and solidarity with those injured. I hope they make a full and speedy recovery.
“Anyone with information should come forward immediately to the police.”