It seems to be adopted in Persian, and there is an Arabic form Sūḳ, which, it is just possible, may have been borrowed and Arabized from the present word. The radical idea of chauk seems to be "four ways" [Skt. chatushka], the crossing of streets at the centre of business. Compare Carfax, and the Quattro Cantoni of Palermo. In the latter city there is a market place called Piazza Ballarò, which in the 16th century a chronicler calls Seggeballarath, or as Amari interprets, Sūḳ-Balharā.
Sanskrit चतुष्क catuṣka "consisting of four" is from catur "four" from Proto-Indo-European *kʷetwer- "four". *kʷetwer- probably became English four - it's thought that the f is by assimilation with the following number, five.
*kʷetwer- became Latin quattuor, then French quatre, which is found in cater-cornered "diagonal". I know the word as the folk-etymologized kitty-corner, a word which indicates something at the opposite corner of an intersection.