The suspect, who was shot dead by police, has not been identified.
Officials say he was a disgruntled lawyer who fired randomly at drivers.
Numerous weapons were found in what is believed to be the suspect's car, Houston's acting police chief said, adding there were no indications of anyone else being involved.
Police say they are also investigating the gunman's apartment and his social media accounts to try and establish a motive.
"The motivation appears to be a lawyer whose relationship with his law firm went bad,", Houston Mayor Sylvester Turner told reporters.
Six victims were taken to hospital, and three were treated at the scene after being shot at while inside their cars, the city's acting Police Chief Martha Montalvo said. One of the victims is in a critical condition.
The shooting comes three days after a shooting at a shopping mall in Washington state, in which five people were killed.
The gunman in that attack, Arcan Cetin, 20, was born in Turkey and is a legal US permanent resident, officials say.
The FBI have said there was no evidence that the shooting there was linked to terrorism.
Nine days ago, a 20-year-old man stabbed 10 people at a Minnesota shopping centre before being shot dead by an off-duty police officer.

A study, published in the journal Nature, showed that mice spending pregnancy in complete darkness had babies with altered eye development.
It indicated tiny quantities of light were needed to control blood vessel growth in the eye.
The researchers hope the findings will aid understanding of eye disorders.
If you could journey inside a mouse or a person, there would not be enough light to see. However, tiny quantities of light do pass through the body.
This effect has already been used to film an infection spreading through the body.
Now scientists - at the University of California, San Francisco, and Cincinnati Children's Hospital Medical Center - believe that body-penetrating light can alter the development of the eye, at least in mice.
Normally, a network of blood vessels known as the hyaloid vasculature is formed to help nourish the retina as it is constructed.
However, the blood vessels would disrupt sight if they remained, so they are later removed - like scaffolding from a finished building.
The researchers said this did not happen when the pregnancy was spent in total darkness.
The critical period was around 16 days - which is very late in mouse gestation, but corresponds to the first trimester in people.
"It's not something subtle here, it's a major effect on the way the retina develops that requires light going through the body," said Prof Richard Lang, from Cincinnati Children's Hospital.
He said it was a "huge surprise" that this was happening.
The researchers hope their findings may aid understanding of human diseases of the eye, as many are down to blood vessels.
Some babies born prematurely develop "retinopathy of prematurity", when the blood vessels in the eye grow abnormally resulting in damage to the retina and a loss of vision.
Prof Lang said: "In retinopathy of prematurity there is overgrowth of blood vessels and that's what you see in these mice."
The researchers showed that light was activating in the mice a protein, melanopsin, which also has a role in regulating the body clock, and is present in people. However, whether the same processes take place in people or other animals is unknown.
Prof Robin Ali, from University College London, said it was a "fascinating study".
He said more research was still needed, but the findings may lead to considerations of light levels during pregnancy and efforts to grow retinas in the laboratory.
He said: "It gives us a whole new aspect to consider in in the development of the retina.
"It illustrates how much we've yet to understand about the eye."
Nine people have been injured in a shooting outside a shopping centre in Houston in the US state of Texas, one of them critically.
[NEXT_CONCEPT]
Light passing through the body and into the womb has an important role in the developing eye, US researchers have discovered.