Smoking will be banned when people cannot maintain a 2-metre (6.5-foot) distance between each other on the islands, which are popular with tourists.
Authorities also imposed new restrictions including the use of masks in public at all times, a limit of 10 people in gatherings and restrictions on nightclub capacity.
"The last few days point to an increase in positive cases ... We will increase checks to make sure people follow the rules because otherwise it will be our health and economy paying the price," regional leader Angel Victor Torres said.
The northwestern region of Galicia imposed a similar ban on smoking on Wednesday.
Officials in both regions said smoking in public places, such as outdoor bar terraces or simply in the street with other pedestrians close, represents a high risk of infection.
Some workers in the bar and restaurant sector that is already stifled by a lack of tourists due to the pandemic sounded alarmed:
"This complicates our lives even more. We already had to tell people to put the face mask on and now we have to tell them that they cannot smoke on terraces. It's going to be complicated," said a bar attendant in the Galician town of Pontevedra who gave his name only as Sergio.
Since lifting one of Europe's strictest lockdowns around seven weeks ago Spain has struggled to keep a lid on new infections, with average daily cases rising from less than 150 in June to more than 1,500 in the first 12 days of August.
There were 99 new cases reported in the Canaries and 107 in Galicia on Thursday, bringing Spain's total new infections to 2,935 and the cumulative total for the country to 337,334.
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