No, and even in China it was only ever limited to the ethnic Han Chinese; during the Qing Dynasty, the Manchu rulers several times tried to outlaw the practice, unsuccessfully.

That said, small feet were still considered more attractive in the rest of the Sinosphere, so even though there was no mutilation as in China, they might take other measures. Traditionally in Korea for instance, noblewomen would often wear socks that were fitted uncomfortably tightly. Here's a quote from Women of Korea: A History from Ancient Times to 1945:

Noblewomen's beoseon [the socks] were made to fit tight, and make the feet appear plump and pretty. Women endured the pain of these ill fitting socks so that their feet would seem like the ‘seeds of a cucumber’ under the long skirts. The socks added to the charm and beauty of her costumes.

Likewise a small gait, which footbinding would have necessitated, was still considered desirable; in Korea and Japan, noblewomen would be expected to walk placing with each step only going just past the last, very delicately, and they'd be trained that way from a young age. So even though no other country went to the extreme of actually binding the feet as they did in China, many of its outcomes were still desired.

I can't prove the negative. But I can say that much has been made in the secondary literature of both Chinese and Western sources to trace the Chinese cultural influences on Tibet, usually reaching back to the seventh century marriages of a Chinese Princess to the Tibetan Emperor to point out how Chinese Buddhism entered Tibet from such an early phase. Later on, Chinese titles from Emperors were bestowed upon various Tibetan rulers, usually spiritual ones like the Karmapa. Chinese tea was (is) extremely popular in Tibet, and there are vestigial parts of Chinese Ch'an Buddhism (what the Japanese call Zen, and the Tibetans refer to as bsam gten) in the Tibetan Dzogchen tradition, an important part of the Nyingma school of Tibetan Buddhism.

That said, I haven't read once about the practice of foot-binding being somethinc that entered the Tibetan cultural sphere. The Tibetans came mostly from a nomadic way of life. Even the settled peoples of the larger towns like Lhasa, Shigatse, Thimphu, and Chengdu, have far-reaching connections with the nomadic communities and as you can imagine, the practice of foot-binding would be a severe hindrance in this way of life. So logic, and the absence of a historical record wouldn't necessarily preclude isolated cases (i.e. there are certainly instances of Tibetan women marrying Chinese men, though whether their mixed daughters ever engaged in the practice, I do not know) but I can rule it out as ever eisting as a large scale practice in the Tibetan Cultural Sphere.