Montezuma is located at 37°35'43N, 100°26'32W (37.595353, -100.442205). According to the United States Census Bureau, the city has a total area of 1.8 km² (0.7 mi²), all land.
As of the census of 2000, there were 966 people, 335 households, and 235 families residing in the city. The population density was 525.3/km² (1,365.0/mi²). There were 362 housing units at an average density of 196.9/km² (511.5/mi²). The racial makeup of the city was 93.58% White, 0.21% Native American, 0.21% Pacific Islander, 3.73% from other races, and 2.28% from two or more races. Hispanic or Latino of any race were 9.21% of the population.
There were 335 households out of which 32.2% had children under the age of 18 living with them, 62.1% were married couples living together, 6.0% had a female householder with no husband present, and 29.6% were non-families. 27.2% of all households were made up of individuals and 13.7% had someone living alone who was 65 years of age or older. The average household size was 2.55 and the average family size was 3.13.
In the city the population was spread out with 25.6% under the age of 18, 8.4% from 18 to 24, 21.6% from 25 to 44, 15.6% from 45 to 64, and 28.8% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 79.9 males. For every 100 females age 18 and over, there were 73.7 males.
The median income for a household in the city was $36,719, and the median income for a family was $41,528. Males had a median income of $31,500 versus $23,750 for females. The per capita income for the city was $19,052. About 5.6% of families and 11.0% of the population were below the poverty line, including 17.8% of those under age 18 and 6.2% of those age 65 or over.