It happened in the 5700 block of Graycliff Drive, in the Pine Trails neighborhood near Uvalde & Wallisville Rd. shortly after 7 p.m. Monday.
Investigators say the armed man was inside the home with a woman and three toddlers, ranging in ages from one to three.
A Harris County SWAT team was able to rescue them after a few hours.
Update on Graycliff Dr: more great work by @HCSOTexas SWAT. They successfully rescued an adult female and three toddlers ranging in ages 1-3 years of age. The male, armed with a machete, was eventually taken into custody. #HouNews— Ed Gonzalez (@SheriffEd_HCSO) August 6, 2019
Sheriff Ed Gonzalez said the man later came out on his own and was taken into custody.
Gonzalez says it appeared the man started a fire before he walked out.
Firefighters responded to the scene and were able to put out the fire.