Jawar, who holds a US passport, is the founder of the independent Oromia Media Network and has a very active presence of social media, with 1.4 million Facebook followers, which he has used in the past to organise strikes and protests.
Two dozen federal police had surrounded the house on Tuesday night, a Reuters witness said, forcing Jawar's bodyguards to leave.
It was not clear why Jawar's house was surrounded, but earlier on Tuesday Abiy, speaking in parliament, had warned unnamed media owners against fomenting unrest.
"Those media owners who don't have Ethiopian passport are playing both ways. When there is peace you are playing here and when we are in trouble you not here," he said.
"We tried to be patient. But if this is going to undermine the peace and existence of Ethiopia, whether you speak Amharic or Oromiffa, we will take measures. You can't play both ways."
Amharic and Oromiffa are the languages of the country's largest ethnic groups.
Jawar, who promotes non-violent activism and an "Oromo first" ideology, returned to Ethiopia from the United States in August last year, a few months after Abiy come to power. Oromo are the country's largest ethnic group, to which both Jawar and Prime Minister Abiy belong.
The young men gathered outside Jawar's house call themselves "Qeerroo", an Oromo term meaning "bachelor" adopted by politically active young men.
Wearing hooded sweatshirts, they shouted "Jawar, Jawar" and "Abiy Down! Abiy Down!"
"I was about to go to bed when I saw Jawar's post that his house was surrounded by security without his knowledge. I called three of my friends and came running and saw more Qeerroos and Qarrees when I arrived at his house," Terefe Waltaji, a 27-year-old student, told Reuters.
Federal Police Spokesman Jeylan Abdi said they had not received any information on what was happening at Jawar's house.
A spokesperson for Abiy did not respond to requests for comment.
Abiy, who won the Nobel prize this month for his peacemaking efforts with longtime enemy Eritrea, came to power in April 2018 and began introducing political and economic reforms.
Those reforms have opened up what was once one of Africa's most repressive nations, but also stoked violence as emboldened regional strongmen build ethnic powerbases and compete over political influence and resources.
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