Morgan's Point is located at 29°40'34" North, 94°59'58" West (29.676368, -94.999580).
According to the United States Census Bureau, the city has a total area of 1.77 mi2 (4.57 km2). 1.61 mi2 (4.18 km2) of it is land and 0.15 mi2 (0.39 km2) of it is covered by water. The total area is 8.56% water.
Morgan's Point is located in the Central Standard Time (CST) timezone, GMT-06:00. It observes Daylight Saving Time (DST).