When BBC Radio 4 celebrated the 80th birthday of the internationally renowned yoga teacher BKS Iyengar, who has died aged 95, the programme started with him answering questions standing on his head. Guruji, as he was known to his followers, said the position was as natural for him as standing on their feet was for others. This was only one of the yoga asanas he taught the pupils from all over the world who flocked to his school in the Indian city of Pune, to the south-east of Mumbai.

More than any other practitioner, Iyengar was responsible for the spread of interest in yoga in the west over the last half-century, having originally introduced the violinist Yehudi Menuhin to the art in the early 1950s. Iyengar used to say "my body is my temple and asanas are my prayers". He lived up to that maxim, keeping himself supremely fit. Yet during his childhood he was, in his words, "a creature of contempt for my people" because of his constant ill-health.

Bellur Krishnamachar Sundararaja Iyengar was born into a family of 13 children, only 10 of whom survived. His father came from the village of Bellur, in the southern Indian state of Karnataka. Iyengar retained his ties with that village and later established education, public health and other social projects there. When Iyengar was five, his father left the village and his job as a primary school headteacher, moving to Bangalore, where he worked as a clerk.

Iyengar was introduced to yoga by one of his brothers-in-law, Tirumalai Krishnamacharya, who ran a yoga school supported by the maharaja of the southern princely state of Mysore, and when Iyengar was 19 sent him to Pune. That city was to become his home for the rest of his life, but his early days there were not auspicious. He was employed by the Deccan Gymkhana Club. The staff there were jealous of his success and one night burned all his equipment. After three years, the club asked Iyengar to leave. Sometimes he could only afford a plate of rice every two or three days. But gradually he came to be better known and more secure.

The break that transformed Iyengar from a comparatively obscure Indian yoga teacher into an international guru came in 1952, when Menuhin visited India. Because Iyengar had taught the famous philosopher Jiddu Krishnamurti, he was asked to go to Bombay to meet Menuhin, who was known to be interested in yoga. Menuhin said he was very tired and could spare only five minutes. Iyengar told him to adopt a relaxing asana, and he fell asleep. After one hour, Menuhin woke refreshed and spent another two hours with Iyengar. Menuhin came to believe that practising yoga improved his playing, and in 1954 invited Iyengar to Switzerland. At the end of that visit, he presented his yoga teacher with a watch on the back of which was inscribed, "To my best violin teacher, BKS Iyengar".

From then on Iyengar visited the west regularly, and schools teaching his system of yoga sprang up all over the world. There are now hundreds of Iyengar yoga centres. During his early travels, he had to face misunderstanding and racism. British immigration officers thought he was some sort of magician and asked him whether he could walk on fire, chew glass or swallow razor blades. A London hotel once refused to accept him as a guest until Menuhin intervened. Even then, Iyengar was told he could not eat in the dining room, and his meals were sent to his room.

Iyengar always insisted that yoga is a spiritual discipline, describing it as "the quest of the soul for the spark of divinity within us". He used to tell his pupils to "be aware that the current of spiritual awareness has to flow in each movement and in each action". As to its wider benefits, he maintained: "Before peace between the nations we have to find peace inside that small nation which is our own being". He regarded much of the yoga that became popular in the west as "nothing more than physical exercise". Unlike western keep-fit exercises, he insisted, yoga must not put any strain on the heart.

Iyengar appeared daunting with his leonine head, mane of hair and formidable eyebrows, which, as he used to say, went in two directions. He had a reputation as a stern teacher, and would insist on his pupils copying his asanas with absolute accuracy, achieving perfect balance. But he also patiently helped those who were having difficulty with their asanas and designed special exercises and equipment for pupils with physical problems. He studied anatomy, psychology and physiology to pioneer modern therapeutic yoga.

He cured one of his pupils, Nivedita Joshi, from a slipped-disc condition that had left her unable to move her hands and legs; she now runs the Iyengar centre in New Delhi. But Iyengar never sought publicity for his achievements and lived a simple life, unmoved by his international renown. Earlier this year he was awarded a state honour, the Padma Vibhushan.

Iyengar's marriage to Ramamani was arranged by his family, and was very happy. He said: "We lived without conflict as if our two souls were one." She died when she was 46 and Iyengar called his yoga school in Pune after her. His son, Prashant, and daughter, Geeta, are now the principal teachers in the Pune yoga school, and his granddaughter, Abhijat, has also taught there. He is also survived by four other daughters.

• Bellur Krishnamachar Sundararaja Iyengar, yoga master, born 14 December 1918; died 20 August 2014