Hundreds of guests at the H10 Costa Adeje Palace Hotel were initially told to stay in their rooms as medical tests were carried out.
The doctor is reportedly from the Lombardy region, where Italian authorities are battling an outbreak.
Global cases of the virus have passed 80,000, the vast majority in China.
Iran, one of the worst-affected nations outside China, on Tuesday said its deputy health minister, Iraj Harirchi, had tested positive for the virus.
The World Health Organization (WHO) said on Monday the world should do more to prepare for a possible pandemic - a situation where an infectious disease spreads easily between people in many countries.
The proportion of infected people who die appears to be between 1% and 2%, although the WHO cautions that the precise mortality rate is not known yet.
What's the latest from the hotel in Tenerife?
Agence France-Presse quoted a health authority spokeswoman, Veronica Martin, as saying that guests at the four-star hotel in the south-west of the island were being monitored for "health reasons and the degree of supervision will be assessed during the day, but so far, we're not talking about quarantine".
One guest posted on Facebook an image of a note put under the door of their room on Tuesday saying: "We regret to inform you that for health reasons, the hotel has been closed down. Until the sanitary authorities warn, you must remain in your rooms."
Another guest, John Turton, told the BBC he and his wife had seen the note but then heard people walking outside and heading to breakfast.
He said: "The hotel has been cordoned off but we're trying to make the best of what's going on. We haven't been given any more information other than the note but we're going to just wait, try and enjoy the holiday and see what happens."
People were now walking around the hotel and using sun loungers, he said, but the police cordon was preventing people from leaving.
Mr Turton said he had not yet been tested.
Fellow Briton Nigel Scotland said he was most concerned that the man who had tested positive had been staying in the hotel for six days, and "during that time, probably five or six hundred people must have left the hotel and gone back to various places in Europe".
The Italian doctor, who had been staying at the hotel with his wife, tested positive on Monday and has been placed in isolation at the University Hospital Nuestra Señora de Candelaria. He will undergo a second test to confirm the virus.
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Previously, Spain had had two confirmed cases, both tourists - one German and one British.
What's happening with the virus globally?
On Tuesday, a plane carrying more than 130 passengers and crew from the Iranian capital, Tehran, to Istanbul was diverted to the Turkish capital, Ankara, amid suspicion of infections on board. Turkey's health minister said all would be quarantined for 14 days.
Iran on Tuesday announced three more deaths, raising fatalities there to 16.
Italy is badly affected, with the largest number of confirmed cases in Europe. It raised that total on Tuesday to 283. Seven people have died.
It announced a series of drastic measures over the weekend to try to contain the outbreak. The regions of Lombardy and Veneto have locked down several small towns. For the next two weeks, 50,000 residents will not be able to leave without special permission.
However, there are signs the virus is spreading, with new cases reported on Tuesday in Tuscany and Sicily. Still, Italian Prime Minister Giuseppe Conte said his country remained safe for travel and tourism.China, the source of the outbreak, still has by far the largest number of infections - more than 77,000 - and deaths, 2,663. The bulk of the cases are in the city of Wuhan.
South Korea's infections rose to 977 on Tuesday, with 10 deaths. Americans have been warned against all but essential travel to the nation.
The White House wants to spend $2.5bn (£1.93bn) fighting the coronavirus, with funds for quarantine, vaccine research and aiding affected states. There are 53 cases in the United States so far.
Japanese media reported that a fourth passenger on the quarantined Diamond Princess cruise liner had died. The country has confirmed more than 850 people are infected, most of them on the liner.
Gulf states, including the UAE and Bahrain, have imposed more flight restrictions in an effort to try to slow the spread of the virus.
And the coronavirus outbreak has continued to hit shares, with Japan's markets slumping in the wake of big falls in London and New York.
What are the symptoms?
The main signs of infection are fever (high temperature) and a cough as well as shortness of breath and breathing difficulties.
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What should I do?
Frequent hand washing with soap or gel, avoiding close contact with people who are ill and not touching your eyes, nose and mouth with unwashed hands can help cut the risk of infection.
Catching coughs and sneezes in a tissue, binning it and washing your hands can minimise the risk of spreading disease.