Paint bombs, bottles and masonry were thrown in the Divis area overnight on Thursday where a large crowd had gathered.
Two of the injured officers had to be taken to hospital after suffering head injuries.
Eight people were arrested for public order offences and a number of streets in the area had to be closed for several hours.
The lord mayor of Belfast, Sinn Féin's Máirtín Ó Muilleoir, condemned it on Twitter.
Disorder also flared at another bonfire in the New Lodge area of north Belfast, where a man attacked police with a sword. Police responded by firing two baton rounds at him.
A statement from the PSNI said: "A thorough investigation is now underway to identify all those involved in the disorder."
West Belfast MP Paul Maskey told UTV the bonfires should not be allowed. He added: "I hope anyone who was injured will make a speedy recovery.
"People do not want to see this happening, they want to live their lives free of these bonfires and they should be a thing of the past. They made a mess of the area and it's totally unacceptable and they cost a lot of money to clear up after."
Lower Falls councillor Colin Keenan, SDLP, said: "For the last number of weeks local people and tourists passing by have been the subject of both verbal and physical assaults.
"Going forward I along with other representatives will continue to champion west Belfast as a place for all to come, visit and enjoy. Anti-social elements will not be allowed to destroy this community which so many of us have worked hard to build."
Earlier on Thursday a female journalist was reportedly attacked at the site of the Divis bonfire.
Meanwhile police have confirmed they are continuing their investigations into reports that a stolen loyalist artwork has been placed on top of it.
The bonfire was erected against the introduction of internment in Northern Ireland in the 1970s.
Around 5,000 people and five bands are expected to take part in an Anti Internment League march through Belfast city centre on Friday evening.
Six loyalist protests from organisations including the Orange Order have been given the go ahead by the Parades Commission.
Organisers of the parade have appealed for calm.
Dee Fennell said: "This is a parade over a human rights issue, not a republican parade and certainly not a dissident republican parade."
A delegation from the DUP has met the PSNI to discuss policing on the night.
"It will be a difficult night," Nelson McCausland MLA said. "This is going to be an affront to all the people who have suffered at the hands of dissident republicans down through the years.
"It is an appalling situation and an affront to decency and democracy."
He added: "I would encourage anyone there to behave peacefully, to make their views known as forcefully and as vocally as they can, but do it always peacefully.
"Violence only plays into the hands of dissident republicans who are intent on violence, they want to provoke a reaction."