The police officers were injured as they tried to restore order for residents when Protestants preparing to march Monday threw missiles and petrol bombs at Catholic protesters who took to the streets overnight.
“This is utterly wrong and I condemn it in the strongest possible terms”, said Northern Ireland Police Chief Superintendent Mark Hamilton.
He accused those involved of being “intent of causing mayhem and destruction”.
Monday, 12 July, is the biggest day in Northern Ireland’s marching season. It marks Prince William of Orange’s victory over the Catholic King James II at the Battle of the Boyne in 1690.
Violence frequently breaks around the date as Catholics try to prevent the marches from taking place.
Last year, 21 police were injured in similar circumstances.
“We have appealed for calm in the run up to the 12 July and we continue to do so," said Hamilton. "We would appeal to anyone with influence in the community to exert it to ensure that the next few days pass off without incident."
A peace agreement was signed in Northern Ireland in 1998 and relative calm has since been maintained.