Portugal confirmed in a statement that Ronaldo is in isolation and not showing symptoms. He was later seen monitoring the team's training session from a terrace of the bedroom in which he is staying in Portugal's City of Football headquarters.
The statement added that following Ronaldo's test, the remaining players in the Portugal squad underwent new tests on Tuesday, which came back negative.
Portugal will be without Ronaldo when they host Sweden on Wednesday in a UEFA Nations League game.
The 35-year-old played all of Sunday's 0-0 draw against world champions France and came closest to scoring when he fired a left-footed strike at goal in added time, but his deflected shot was well saved by France goalkeeper Hugo Lloris.
He also started in Portugal's goalless draw against Spain in Lisbon last week, a game that marked his 200th appearance for his country at both youth and senior level.
On Monday, Ronaldo posted a picture of himself with the Portugal squad alongside the message: "United on and off the field!"
Ronaldo's mother, Dolores Aveiro, posted a photograph of him wearing the Portugal jersey with the message: "God gives great battles to great warriors and it is one more war that you will win son."
"Unfortunately, we already had two players test positive. And today we have it again. It's very abnormal," Portugal manager Fernando Santos told a news conference on Tuesday.
Santos said Ronaldo first tested positive on Monday night.
"Yesterday [Monday] night, after the test, Ronaldo and all the players went into isolation. During the night, we heard about the positive test and in the morning Ronaldo was tested again, as were the other players. He's in the room, he's fine and asymptomatic. I don't even understand what happened to him," he said. "These are difficult times and, at the beginning, there is always room for apprehension and anxiety. Then, everything calms down and everything goes back to normal. Other players are negative and life goes on."
Santos assured reporters the team has been taking every precaution to prevent infections.
"This COVID-19 question, besides being sad from a human standpoint, [is] also [sad] because we have done everything that we've been told to do. For us, health is very important," Santos said. "Since Monday, we have been completely confined here. The staff and players entered and no one else entered. No one from the outside has entered.
"In the first stage [international window] we had no problems, but here it has happened and it was not due to noncompliance with the rules. This is not where the virus attacked. This is how things are. Players have been concerned with keeping the rules safe. We did seven tests, every day we were tested, so obviously this is what leaves us this taste that we did everything and it happened. Unfortunately, nobody really knows what this issue is. I didn't notice. We left, the bus, airport ... We complied with the rules of the DGS [health authorities]."
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He was among several Juve players who joined up with their national teams last week and did not remain in quarantine in Turin after Juve reported that two staff members had tested positive for the coronavirus.
Juve announced that the squad isolated at Juve's hotel as per the protocol by Turin's health authorities.
Ronaldo did test negative in one test carried out in Turin but left Juve's hotel on Monday before the second test was carried out.
Juventus players weren't allowed by the local health authorities to leave the hotel until Oct. 7, two days after Ronaldo had joined Portugal.
The Turin health authorities have reported those Juve players who left the quarantine early to the local prosecutor's office to determine whether any infraction of the protocol was committed.
Portugal president Marcelo Rebelo de Sousa addressed the news later on Tuesday, telling reporters he has confidence the team will be fine without Ronaldo.
"I spoke to the Portuguese Football Federation, which has a testing system done every day. The players come from different countries. There is an immediate control of their situation. What I was told is that there are no other individuals that have tested positive," De Sousa said.
"I wished him well and tomorrow we will be supporting the team there, knowing that there have already been recent games in this competition in which we played without Cristiano Ronaldo and we still won and played a great game. It is obvious that it implies quarantine, which is a personal, family and professional sacrifice."
Ronaldo is the 76th Serie A player to have tested positive for COVID since the pandemic started.
In March, former Real Madrid star and his agent, Jorge Mendes, helped out by financing hospitals in Portugal.
Last month, Ronaldo became the second male player to score 100 international goals as he scored twice in a 2-0 UEFA Nations League win against Sweden.
He is second in the all-time list of leading international scorers behind Iran's Ali Daei, who scored 109 in his career.
ESPN's Adriana Garcia contributed to this report.