The team said the 52-year-old Kubiak suffered a transient ischemic attack at halftime of Sunday's loss to Indianapolis. He was released from the hospital on Tuesday and is expected to make a full recovery.
"I've been through an ordeal and my focus now is to get back to good health," Kubiak said in a statement released by the team. "Doctors have told me I will make a full recovery."
Kubiak collapsed on the field and was rushed to a hospital. The Texans blew an 18-point lead without him and the 27-24 setback was the team's sixth straight loss.
A transient ischemic attack, or TIA, occurs when blood flow to the brain is briefly interrupted, typically by a blood clot or narrowed blood vessels. TIAs are often called mini-strokes and can cause stroke-like symptoms including sudden dizziness, numbness, vision loss or unconsciousness, though symptoms last only a few minutes or a few hours and no permanent brain damage occurs. TIAs are often a warning sign for a future stroke.
Former Cincinnati Reds manager Dusty Baker had a mini-stroke in 2012. Baker, who was initially hospitalized for an irregular heartbeat, returned to manage the Reds less than two weeks after his mini-stroke.
Houston didn't identify an interim coach as it prepared for Sunday's game at Arizona. Defensive coordinator Wade Phillips, a former head coach for Dallas, took over after Kubiak was taken to the hospital and he ran Houston's practice on Monday. Offensive coordinator Rick Dennison likely will take over the play-calling duties if Kubiak isn't back by Sunday.
The Texans don't think things will change much with Dennison calling the plays.
"If he's not here, then (Dennison) can handle it," receiver Andre Johnson said.
Kubiak's health problems are the latest blow to a team already in disarray in an underperforming season filled with numerous injuries and the benching of quarterback Matt Schaub. The six-game skid is tied for the longest losing streak in Texans history.
Now the Texans will try to regroup and adjust to Kubiak's likely absence on Sunday.
"It's been frustrating, especially after the past two seasons and the expectations," Johnson said. "But if you don't go out and play the way you're supposed to play you're not going to win. And we didn't do that so that's why we haven't been winning ... somehow some way we've got to go out and fix the mistakes we've been making and try to win a game."
Players said they believe Houston's assistant coaches will prepare them well for Sunday's game with Kubiak out.
"I think we're in great hands with whoever has to step up," linebacker Joe Mays said. "You're in great hands because we have a great group of coaches."
Kubiak was the second NFL coach with a severe medical issue this past weekend. Denver Broncos coach John Fox underwent heart surgery in North Carolina on Monday after being hospitalized on Saturday. Fox felt dizzy last week and doctors recommended immediate aortic valve replacement surgery.
Kubiak was hired in 2006 and is working under a three-year contract that runs through 2014. An eighth-round pick out of Texas A&M, he spent nine years as John Elway's backup in Denver and has made his mark as an offensive guru and quarterbacks mentor.