See all shopping in Knoxville Knoxville for: Adventure, Food And Dining, Art And Culture, Nightlife, Spa, History, First Timers, Family, Romance, Shopping Market Square Farmer's Market About Market Square Farmer's Market, +1 865 405-3135, [45]. Harking back to the square's original function, the Market Square District Association hosts a farmer's market each Wednesday (11AM-2PM) and Saturday (9AM-1PM.) Add to Wish List