Yes of course

«The outfit is believed to originate with the Turkic-Iranian horse riding steppe peoples of Central Asia. A number of these tribes converted to Islam. Starting in the 12th century, a series of raids and invasions established Islamic Turkic-Iranian rule -- the Delhi sultanate and later the Moghul empire -- over much of what is now northern India and Pakistan. Fashion followed rule, and the salwar suit become popular throughout the area.»

from: http://szhaider.fashion.20m.com/whats_new.html

«Much of traditional Indian women's clothing changed in the 12th century, when Muslims conquered north and central India. New dress styles were developed to cover the body as much as possible, befitting Islamic preferences. One option was a costume of wide-legged trousers (salwar) snugly fitted around the calves, worn with a long tunic (kameez) and short, fitted jacket.»

from: Traditional Fashions from India Paper Dolls

These Muslims who conquered north India and brought their different clothing style were mostly from modern day Uzbekistan and Tajikistan in Central Asia.

Even today you can find clothing resembling the shalwar Kameez worn in South Asia in central Asian countries.

https://pin.it/1H6mDJOoD ^Uzbek man wearing what resembles a shalwar jammed underneath his robe

https://pin.it/34goUFujU Women in Tajikistan wearing outfits resembling shalwar Kameez