He was speaking five days after rioting broke out in Dublin in the aftermath of a school knife attack.
Three children and a school care assistant were stabbed outside a city centre primary school on Thursday afternoon.
A five-year-old girl and the care assistant were very seriously wounded.
Mr Varadkar confirmed the man suspected of carrying out the attack is an Irish citizen who has been in Ireland for 20 years, but was not born in the state.
Government sources have confirmed to the BBC that the man is believed to be from Algeria.
Speaking in the Dáil (Irish Parliament), Mr Varadkar also confirmed the injured five-year-old girl was born in Ireland to non-national parents.
She was stabbed in the chest and was critically ill for several days but she is now said to be in a serious, but stable condition in hospital.
The riot erupted within hours of the school stabbing, with many people on social media using the attack to criticise the government’s immigration policies.
The head of Irish police said the violence was stoked by those influenced by “far right ideology”.
“I really would ask people to try and avoid connecting crime with migration. It’s not right,” Mr Varadkar told the Dáil.
“Yes, of course, people who are migrants might commit crimes, just as people who aren’t commit crimes.”
Mr Varadkar said in a country of 5.3m people with hundreds of thousands of migrants, there are going to be a few of them who commit terrible crimes.
“Just as there are people born and bred in Ireland who commit terrible crimes every day, including murders,” he added.
Clashes in Dublin after knife attack outside school
The children were stabbed as they lined up after class at Gaelscoil Choláiste Mhuire on Parnell Square at lunchtime on Thursday.
Mr Varadkar repeated his praise for the people who intervened to bring the knife attack to an end, pointing out most of them had been born abroad.
“Of the five or six people who intervened to stop the attack, four of those six are migrants to this country,” he said.
“It’s totally wrong to try and make out that there’s a connection between crime and migration based on what happened on Parnell Street.”
The riot, which involved up to 500 people, began on Thursday evening and resulted in gardaí being attacked, vehicles being burned and shops being looted.
Mr Varadkar said the violence had caused fear among Ireland’s migrant communities.
“There are a lot of people, particularly people of colour in Ireland who are very afraid because of what happened on Thursday night,” he said.
He argued that migration “is a good thing for Ireland” and that people need to understand the impact of their words on migrant workers.
“When I go into any hospital in Ireland, including ones that I’ve worked in, I see a very diverse workforce,” he said.
“Many of the doctors and nurses and other staff who looked after the stabbing victims come from other parts of the world.”
Earlier, an Irish government minister told reporters that Dublin is “not safe enough” following last weeks riots in the city.
Eamon Ryan, who leads the Green Party, made the remarks on his way into a Cabinet meeting during which garda (Irish police) resources were discussed.
Speaking to Irish brodacaster RTÉ and other media, Mr Ryan said: “I love Dublin, I grew up, [was] born and raised in this city.
“It has great qualities, great characteristics, but as long as my neighbour doesn’t feel secure, then I’m insecure too.
“We need to keep the decency and the culture and the values that are real Dublin values in my mind, not be intimidated by the sort of antics we saw last week.”
The Green leader added that “we can make it safe and we need to make it safe”.
Some concern had been expressed about the speed of the police response to the disorder.
The operation saw the largest ever number of riot-trained officers deployed, with staff from all over the country travelling to Dublin to provide support.
The main opposition party, Sinn Féin, criticised head of Ireland’s police force, Garda Commissioner Drew Harris, and the Minister for Justice Helen McEntee
On Tuesday, Ms McEntee announced she has ordered a review to identify changes needed to help frontline gardaí deal with serious public order incidents.
“I have asked for clarity on use of force because I don’t want gardaí looking over their shoulder when they feel force is necessary,” she said.
She has asked the Policing Authority https://gimanalagiyakan.com to review how gardaí could be further supported, including with the possible provision of non-lethal equipment.