Map of Zip Code 78537 Border. Zip Code 78537 is located in the state of Texas in the Brownsville metro area. Zip code 78537 is primarily located in Hidalgo County. The official US Postal Service name for 78537 is DONNA, Texas. Portions of zip code 78537 are contained within or border the city limits of Donna, TX, Scissors, TX, Midway South, TX, Midway North, TX, La Blanca, TX, Elsa, TX, Alamo, TX, Muniz, TX, Weslaco, TX, San Carlos, TX, South Alamo, TX, and San Juan, TX. The area code for zip code 78537 is 956.