Footage circulating on social media shows the wind and waves tearing railings from what are understood to be the balconies of holiday apartments.
Local media report dozens of people were evacuated from their lodgings at the weekend in the popular tourist town on what is the largest of the Canary Islands.
It is unclear this stage how many Brits, if any were affected. The Foreign Office has not issued any updated guidance for the region.
Alvaro Davila, mayor of the municipality of Tacoronte which Mesa del Mar is part of, said 65 apartments in two blocks facing the ocean had been evacuated, the Mirror reports.
He added despite another 39 people being evacuated from two buildings in Garichico, also on the north coast, there were no reports of any injuries.
The Spanish meteorological agency had issued an orange alert, although this has been downgraded to yellow. It had been due to remain in place until Monday morning.