Spanish media said a homeless Bulgarian man had been arrested in the town of Los Cristianos.
Witnesses said a man entered a Chinese supermarket in a shopping centre and stabbed then beheaded the 62-year-old woman. He is said to have dropped the head outside before being tackled.
A local official said the man appeared to choose his victim at random.
Witnesses said the man entered the Chinese supermarket in Valdes Shopping Centre and attacked the woman without saying a word.
"Apparently this gentleman without any motive or any reason... entered the shop and then cut this woman's neck and took the head in his hand outside," said local councillor Manuel Reveron.
A security guard then managed to wrestle the man to the ground, he said.
"I parked my car and saw a man running out with something bloody in his hands and a security guard chasing him," one witness was quoted as telling local radio.
"He threw it to the ground, it almost hit me and what he had been carrying was a woman's head."
In a video posted on YouTube, Colin Kirby of Tenerifemagazine.com said security guards held down the suspect until the police arrived.
"The security and the police had to hold people off - they were queuing up - they were trying basically to kick the hell out of the guy," he said.
Police sources told Spanish media the suspect had a police record.
현재 시간 BBC뉴스 중
스페인 한 도시에 있는 중국마트에 있던 영국 여성의 목을 잘라서 그걸 밖에 던져버렸다네요.불가리아 부랑자라는데... 말도 없이...이유나 동기도 없이....끔찍하네요. 진짜 엽기....가끔 이런 사건보면 유럽 쪽 아그들이 잔인한 면이 많은듯...갑자기 호스텔이 생각나네요.-0-