In an interview with Voice of America's Amharic service, the actor said the Ethiopian security forces had carried out "atrocious actions" and he had decided not to return home until the "regime is changed".
"It is sad to respond with bullets to people's demand for their rights," he added.
At the root of the recent demonstrations in Amhara is a request by representatives from the Welkait Amhara Identity Committee that their land, which is currently administered by the Tigray regional state, be moved into the neighbouring Amhara region.
The Oromo people in Ethiopia have also been protesting against the government, saying they have been excluded politically and economically.
During the Rio Olympics, marathon runner Feyisa Lilesa crossed the line in second place with his arms above his head in solidarity with Oromo activists.
He said he wanted to seek asylum after the high-profile anti-government protest, and he is now in the US.
At a meeting of the Israel Bar Association in Tel Aviv on Tuesday, Mr Alsheich was asked why Ethiopian-Israelis appeared to be singled out by his force.
"Studies the world over, without exception, have shown that immigrants are invariably more involved in crime than others, and this should not come as a surprise," he responded.
Research had also shown that young people in general were more involved in crime and that "when the two come together, there's a situation in which a given community is more involved than others in crime, statistically speaking", he added.
The commissioner said this had been the case "in all the waves of immigration" to Israel, and "also with regard to [Israeli] Arabs or [Palestinians in] East Jerusalem".
"When a police officer comes across a suspicious person, his brain suspects him more than if he were someone else. It's natural," he continued.
"We know this. We have started to deal with this."
The Israel Association for Ethiopian Jews said the remarks were "intolerable" and reinforced "stereotypes that portray all young people from our community as delinquents and criminals".
The legal advocacy group Tebeka accused Mr Alsheich of "in effect declaring that the whole community was a community of criminals" and giving "justification to the police for their systemic racism and violence toward Ethiopian-Israelis".
"We are not migrant workers, we are Jews who returned to their country after some 2,500 years in exile," Gadi Yibarkan, an activist who was involved in last year's protests, told the Times of Israel.
He added that the commissioner had made it seem "understandable that police officers deal violently with black people and Arabs".
Following the criticism, the police force issued a statement saying that Mr Alsheikh "had no intention of offending Israelis of Ethiopian origin".
It added: "The remarks were said, openly, with the intention of correcting and improving [the force]."