The aircraft had set off from the neighbouring island of Gran Canaria in the midst of a wild storm which has swept through the Canary archipelago over the past two days.
According to Spain's Airport Association AENA, the Binter Canarias aircraft veered from the runway at 18.50 on Wednesday "due to an excess of water", causing its tyres to experience aquaplaning.
None of the 51 passengers and four crew members on board were injured in the incident, although airport sources later confirmed one person had suffered a sprained ankle.
The landing strip was closed for two hours after the incident as airport staff ascertained if it was too flooded for other aircraft to attempt landing.
Numerous other flights to and from different Canary Islands have been cancelled over the past two days due to the heavy rainfall and winds of up to 120kmh.
Strong winds and heavy rainfall will continue to batter the archipelago on Thursday and Friday, Spain's meteorological agency AEMET has announced.
— Cande Padilla (@cande64) December 11, 2013
Los Rodeos, Tenerife's northern airport, was dogged for years by its reputation as the site of the most deadly air disaster of all time.
In 1977,two planes collided on the runway due in part to the lack of visibility caused by the frequent fog which settles in the airport's hilly location.
A total of 583 people were killed, the highest number of fatalities —excluding ground fatalities— of any single accident in aviation history.