Kubiak collapsed to his knees while running off the field during halftime of the Texans' 27-24 loss to Indianapolis Sunday at Reliant Stadium.
He was taken off the field on a stretcher and transported to a local hospital as a precaution.
Texans General Manager Rick Smith said Kubiak underwent testing after being admitted and will remain hospitalized for at least the next 24 hours.
"Our primary concern is of course with Gary's health and well-being," Smith said. "There have been so many people throughout the city and across the country that have reached out to express their love and support and we are thankful for everyone's thoughts and prayers.
"Gary is alert, coherent and in good spirits. He is continuing to be evaluated and monitored."
Defensive coordinator Wade Phillips took over as interim coach for the Texans, who blew a big lead after Kubiak's departure and suffered a sixth straight loss.