Lava has been pouring downhill from the Cumbre Vieja volcano on the Canary island since it erupted on Sunday (19 September).
According to the BBC, citing local officials, around 5,500 locals have been evacuated. No casualties have been reported so far following evacuation orders for four villages.
Around 500 tourists have also reportedly been evacuated by local authorities.
On Monday (20 September), Tui said: "We are aware that on Sunday, 19 September, at approximately 15.15hrs, a volcano erupted in the Cumbre Vieja national park on the island of La Palma.
"We can confirm that the affected areas of the island have no impact on our customers and our flights are due to operate as planned.
"We will continue to monitor the situation closely and will contact customers directly should their holiday be impacted."
The UK Foreign Office confirmed the immediate areas of Los Llanos de Aridane, Tazacorte and El Paso, including Cabeza de Vaca, have been evacuated.
In an a travel alert issued on Monday evening (20 September), it said: "If you are in an affected area you should follow the advice of local authorities, including social media updates from Cabildo de La Palma.
"If you are planning to travel to the island imminently you are encouraged to contact your tour operators and/or airlines."