Authorities say the male cyclist was in fear for his life and fired shots at the driver.
It happened in the 5000 block of Jefferson Street around 2:19 p.m.
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Police said the driver told the bicyclists that they could not be riding around in the neighborhood. The violent confrontation happened a short time later.
The male cyclist had a gun on him and shot the driver, police said.
"He was in fear of his life, and he was trying to defend himself," a police officer at the scene said of the bicyclist.
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Police also said the driver had no right to tell the bicyclists they could not ride around in the area.
The driver, identified as Jose Angel Hernandez, has been charged with aggravated assault with a deadly weapon, according to Houston police.
The bicyclists are OK, according to authorities. The driver was taken to Ben Taub Hospital. His condition was not known.