Member Details Asian Market Share: Grocery Asian Market 2425 Mchenry Avenue Suite A Modesto, California 95350 (209) 578-0147 Facebook Twitter Hours: Monday-Saturday 9am-7pm Sunday 9am-6pm About Map About Asian grocery store, offering a variety of groceries and household products from multiple Asian countries. Directions On Mchenry Avenue in the shopping center between Floyd and Briggsmore. Located between Dollar Store and Party City. What's Nearby? Distance: 5 10 15 20 25 50 mi.