Two officers have been suspended and the incident is being investigated.
Israeli President Reuven Rivlin blamed a "handful of violent trouble-makers" for Sunday's violence but said Ethiopian Jews' grievances had to be addressed.
The protests, he added, exposed "the pain of a community crying out over a sense of discrimination, racism, and of being unanswered. We must look directly at this open wound."
On Monday, Israeli Prime Minister Benjamin Netanyahu will meet the soldier who appeared in the video, as well as Ethiopian community leaders.
'Not prepared to wait'
On Sunday, protests started peacefully as demonstrators blocked a busy road. Many walked with their hands held together in the air, to signify handcuffs. But the demonstration became more violent as night fell.
Some protesters threw stones, bottles and chairs and tried to enter the municipality building.
At least 46 police and seven protesters were hurt, officials said. Dozens of protesters were arrested, police said.
One demonstrator told Israel's Channel 10 television channel: "Our parents were humiliated for years.
"We are not prepared to wait any longer to be recognised as equal citizens. It may take a few months, but it will happen."
Tel Aviv police chief Yohanan Danino told Channel 10: "The use of violence by a small minority of the many protesters does not serve their struggle.
"Whoever harms police or civilians will be brought to justice.''
Ethiopian Jews living in Israel have long complained of discrimination, and similar protests in 2012 followed reports that some Israeli landlords were refusing to rent out their properties to Ethiopian Jews.
Ethiopian Israeli Jews' income is considerably lower than the general population, and they are much more likely to face limited educational opportunities and to end up in prison, according to The Ethiopian National Project, a non-governmental organisation which assists Ethiopian Jews in Israel.
Tens of thousands of Ethiopian Jews were airlifted to Israel in secret operations in the 1980s and 1990s to escape famine and civil war. There are now around 135,000 Ethiopian Jews living in Israel.