Workers in Santa Cruz province, which also covers La Palma, La Gomera and El Hierro, started their two-day walkout on Thursday (17 April).
The action will reportedly affect around 80,000 workers. It comes after a new deal concerning pay and conditions was rejected.
Elsewhere in the Canaries, workers in Las Palmas province, which includes Gran Canaria, Lanzarote and Fuerteventura, have come to terms.
In an update to is travel advice for Spain issued on Thursday morning, the FCDO advised holidaymakers to stay in touch with their travel provider.